<!DOCTYPE html><html><head>
      <title>06</title>
      <meta charset="utf-8">
      <meta name="viewport" content="width=device-width, initial-scale=1.0">
      
      <style>
      /*!
 * reveal.js
 * http://revealjs.com
 * MIT licensed
 *
 * Copyright (C) 2018 Hakim El Hattab, http://hakim.se
 */
/*********************************************
 * RESET STYLES
 *********************************************/
html, body, .reveal div, .reveal span, .reveal applet, .reveal object, .reveal iframe,
.reveal h1, .reveal h2, .reveal h3, .reveal h4, .reveal h5, .reveal h6, .reveal p, .reveal blockquote, .reveal pre,
.reveal a, .reveal abbr, .reveal acronym, .reveal address, .reveal big, .reveal cite, .reveal code,
.reveal del, .reveal dfn, .reveal em, .reveal img, .reveal ins, .reveal kbd, .reveal q, .reveal s, .reveal samp,
.reveal small, .reveal strike, .reveal strong, .reveal sub, .reveal sup, .reveal tt, .reveal var,
.reveal b, .reveal u, .reveal center,
.reveal dl, .reveal dt, .reveal dd, .reveal ol, .reveal ul, .reveal li,
.reveal fieldset, .reveal form, .reveal label, .reveal legend,
.reveal table, .reveal caption, .reveal tbody, .reveal tfoot, .reveal thead, .reveal tr, .reveal th, .reveal td,
.reveal article, .reveal aside, .reveal canvas, .reveal details, .reveal embed,
.reveal figure, .reveal figcaption, .reveal footer, .reveal header, .reveal hgroup,
.reveal menu, .reveal nav, .reveal output, .reveal ruby, .reveal section, .reveal summary,
.reveal time, .reveal mark, .reveal audio, .reveal video {
  margin: 0;
  padding: 0;
  border: 0;
  font-size: 100%;
  /* font: inherit; */
  vertical-align: baseline; }

.reveal article, .reveal aside, .reveal details, .reveal figcaption, .reveal figure,
.reveal footer, .reveal header, .reveal hgroup, .reveal menu, .reveal nav, .reveal section {
  display: block; }

/*********************************************
 * GLOBAL STYLES
 *********************************************/
html,
body {
  width: 100%;
  height: 100%;
  overflow: hidden; }

body {
  position: relative;
  line-height: 1;
  background-color: #fff;
  color: #000; }

/*********************************************
 * VIEW FRAGMENTS
 *********************************************/
.reveal .slides section .fragment {
  opacity: 0;
  visibility: hidden;
  transition: all .2s ease; }
  .reveal .slides section .fragment.visible {
    opacity: 1;
    visibility: inherit; }

.reveal .slides section .fragment.grow {
  opacity: 1;
  visibility: inherit; }
  .reveal .slides section .fragment.grow.visible {
    -webkit-transform: scale(1.3);
            transform: scale(1.3); }

.reveal .slides section .fragment.shrink {
  opacity: 1;
  visibility: inherit; }
  .reveal .slides section .fragment.shrink.visible {
    -webkit-transform: scale(0.7);
            transform: scale(0.7); }

.reveal .slides section .fragment.zoom-in {
  -webkit-transform: scale(0.1);
          transform: scale(0.1); }
  .reveal .slides section .fragment.zoom-in.visible {
    -webkit-transform: none;
            transform: none; }

.reveal .slides section .fragment.fade-out {
  opacity: 1;
  visibility: inherit; }
  .reveal .slides section .fragment.fade-out.visible {
    opacity: 0;
    visibility: hidden; }

.reveal .slides section .fragment.semi-fade-out {
  opacity: 1;
  visibility: inherit; }
  .reveal .slides section .fragment.semi-fade-out.visible {
    opacity: 0.5;
    visibility: inherit; }

.reveal .slides section .fragment.strike {
  opacity: 1;
  visibility: inherit; }
  .reveal .slides section .fragment.strike.visible {
    text-decoration: line-through; }

.reveal .slides section .fragment.fade-up {
  -webkit-transform: translate(0, 20%);
          transform: translate(0, 20%); }
  .reveal .slides section .fragment.fade-up.visible {
    -webkit-transform: translate(0, 0);
            transform: translate(0, 0); }

.reveal .slides section .fragment.fade-down {
  -webkit-transform: translate(0, -20%);
          transform: translate(0, -20%); }
  .reveal .slides section .fragment.fade-down.visible {
    -webkit-transform: translate(0, 0);
            transform: translate(0, 0); }

.reveal .slides section .fragment.fade-right {
  -webkit-transform: translate(-20%, 0);
          transform: translate(-20%, 0); }
  .reveal .slides section .fragment.fade-right.visible {
    -webkit-transform: translate(0, 0);
            transform: translate(0, 0); }

.reveal .slides section .fragment.fade-left {
  -webkit-transform: translate(20%, 0);
          transform: translate(20%, 0); }
  .reveal .slides section .fragment.fade-left.visible {
    -webkit-transform: translate(0, 0);
            transform: translate(0, 0); }

.reveal .slides section .fragment.fade-in-then-out,
.reveal .slides section .fragment.current-visible {
  opacity: 0;
  visibility: hidden; }
  .reveal .slides section .fragment.fade-in-then-out.current-fragment,
  .reveal .slides section .fragment.current-visible.current-fragment {
    opacity: 1;
    visibility: inherit; }

.reveal .slides section .fragment.fade-in-then-semi-out {
  opacity: 0;
  visibility: hidden; }
  .reveal .slides section .fragment.fade-in-then-semi-out.visible {
    opacity: 0.5;
    visibility: inherit; }
  .reveal .slides section .fragment.fade-in-then-semi-out.current-fragment {
    opacity: 1;
    visibility: inherit; }

.reveal .slides section .fragment.highlight-red,
.reveal .slides section .fragment.highlight-current-red,
.reveal .slides section .fragment.highlight-green,
.reveal .slides section .fragment.highlight-current-green,
.reveal .slides section .fragment.highlight-blue,
.reveal .slides section .fragment.highlight-current-blue {
  opacity: 1;
  visibility: inherit; }

.reveal .slides section .fragment.highlight-red.visible {
  color: #ff2c2d; }

.reveal .slides section .fragment.highlight-green.visible {
  color: #17ff2e; }

.reveal .slides section .fragment.highlight-blue.visible {
  color: #1b91ff; }

.reveal .slides section .fragment.highlight-current-red.current-fragment {
  color: #ff2c2d; }

.reveal .slides section .fragment.highlight-current-green.current-fragment {
  color: #17ff2e; }

.reveal .slides section .fragment.highlight-current-blue.current-fragment {
  color: #1b91ff; }

/*********************************************
 * DEFAULT ELEMENT STYLES
 *********************************************/
/* Fixes issue in Chrome where italic fonts did not appear when printing to PDF */
.reveal:after {
  content: '';
  font-style: italic; }

.reveal iframe {
  z-index: 1; }

/** Prevents layering issues in certain browser/transition combinations */
.reveal a {
  position: relative; }

.reveal .stretch {
  max-width: none;
  max-height: none; }

.reveal pre.stretch code {
  height: 100%;
  max-height: 100%;
  box-sizing: border-box; }

/*********************************************
 * CONTROLS
 *********************************************/
@-webkit-keyframes bounce-right {
  0%, 10%, 25%, 40%, 50% {
    -webkit-transform: translateX(0);
            transform: translateX(0); }
  20% {
    -webkit-transform: translateX(10px);
            transform: translateX(10px); }
  30% {
    -webkit-transform: translateX(-5px);
            transform: translateX(-5px); } }
@keyframes bounce-right {
  0%, 10%, 25%, 40%, 50% {
    -webkit-transform: translateX(0);
            transform: translateX(0); }
  20% {
    -webkit-transform: translateX(10px);
            transform: translateX(10px); }
  30% {
    -webkit-transform: translateX(-5px);
            transform: translateX(-5px); } }

@-webkit-keyframes bounce-down {
  0%, 10%, 25%, 40%, 50% {
    -webkit-transform: translateY(0);
            transform: translateY(0); }
  20% {
    -webkit-transform: translateY(10px);
            transform: translateY(10px); }
  30% {
    -webkit-transform: translateY(-5px);
            transform: translateY(-5px); } }

@keyframes bounce-down {
  0%, 10%, 25%, 40%, 50% {
    -webkit-transform: translateY(0);
            transform: translateY(0); }
  20% {
    -webkit-transform: translateY(10px);
            transform: translateY(10px); }
  30% {
    -webkit-transform: translateY(-5px);
            transform: translateY(-5px); } }

.reveal .controls {
  display: none;
  position: absolute;
  top: auto;
  bottom: 12px;
  right: 12px;
  left: auto;
  z-index: 1;
  color: #000;
  pointer-events: none;
  font-size: 10px; }
  .reveal .controls button {
    position: absolute;
    padding: 0;
    background-color: transparent;
    border: 0;
    outline: 0;
    cursor: pointer;
    color: currentColor;
    -webkit-transform: scale(0.9999);
            transform: scale(0.9999);
    transition: color 0.2s ease, opacity 0.2s ease, -webkit-transform 0.2s ease;
    transition: color 0.2s ease, opacity 0.2s ease, transform 0.2s ease;
    z-index: 2;
    pointer-events: auto;
    font-size: inherit;
    visibility: hidden;
    opacity: 0;
    -webkit-appearance: none;
    -webkit-tap-highlight-color: transparent; }
  .reveal .controls .controls-arrow:before,
  .reveal .controls .controls-arrow:after {
    content: '';
    position: absolute;
    top: 0;
    left: 0;
    width: 2.6em;
    height: 0.5em;
    border-radius: 0.25em;
    background-color: currentColor;
    transition: all 0.15s ease, background-color 0.8s ease;
    -webkit-transform-origin: 0.2em 50%;
            transform-origin: 0.2em 50%;
    will-change: transform; }
  .reveal .controls .controls-arrow {
    position: relative;
    width: 3.6em;
    height: 3.6em; }
    .reveal .controls .controls-arrow:before {
      -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(45deg);
              transform: translateX(0.5em) translateY(1.55em) rotate(45deg); }
    .reveal .controls .controls-arrow:after {
      -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(-45deg);
              transform: translateX(0.5em) translateY(1.55em) rotate(-45deg); }
    .reveal .controls .controls-arrow:hover:before {
      -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(40deg);
              transform: translateX(0.5em) translateY(1.55em) rotate(40deg); }
    .reveal .controls .controls-arrow:hover:after {
      -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(-40deg);
              transform: translateX(0.5em) translateY(1.55em) rotate(-40deg); }
    .reveal .controls .controls-arrow:active:before {
      -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(36deg);
              transform: translateX(0.5em) translateY(1.55em) rotate(36deg); }
    .reveal .controls .controls-arrow:active:after {
      -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(-36deg);
              transform: translateX(0.5em) translateY(1.55em) rotate(-36deg); }
  .reveal .controls .navigate-left {
    right: 6.4em;
    bottom: 3.2em;
    -webkit-transform: translateX(-10px);
            transform: translateX(-10px); }
  .reveal .controls .navigate-right {
    right: 0;
    bottom: 3.2em;
    -webkit-transform: translateX(10px);
            transform: translateX(10px); }
    .reveal .controls .navigate-right .controls-arrow {
      -webkit-transform: rotate(180deg);
              transform: rotate(180deg); }
    .reveal .controls .navigate-right.highlight {
      -webkit-animation: bounce-right 2s 50 both ease-out;
              animation: bounce-right 2s 50 both ease-out; }
  .reveal .controls .navigate-up {
    right: 3.2em;
    bottom: 6.4em;
    -webkit-transform: translateY(-10px);
            transform: translateY(-10px); }
    .reveal .controls .navigate-up .controls-arrow {
      -webkit-transform: rotate(90deg);
              transform: rotate(90deg); }
  .reveal .controls .navigate-down {
    right: 3.2em;
    bottom: 0;
    -webkit-transform: translateY(10px);
            transform: translateY(10px); }
    .reveal .controls .navigate-down .controls-arrow {
      -webkit-transform: rotate(-90deg);
              transform: rotate(-90deg); }
    .reveal .controls .navigate-down.highlight {
      -webkit-animation: bounce-down 2s 50 both ease-out;
              animation: bounce-down 2s 50 both ease-out; }
  .reveal .controls[data-controls-back-arrows="faded"] .navigate-left.enabled,
  .reveal .controls[data-controls-back-arrows="faded"] .navigate-up.enabled {
    opacity: 0.3; }
    .reveal .controls[data-controls-back-arrows="faded"] .navigate-left.enabled:hover,
    .reveal .controls[data-controls-back-arrows="faded"] .navigate-up.enabled:hover {
      opacity: 1; }
  .reveal .controls[data-controls-back-arrows="hidden"] .navigate-left.enabled,
  .reveal .controls[data-controls-back-arrows="hidden"] .navigate-up.enabled {
    opacity: 0;
    visibility: hidden; }
  .reveal .controls .enabled {
    visibility: visible;
    opacity: 0.9;
    cursor: pointer;
    -webkit-transform: none;
            transform: none; }
  .reveal .controls .enabled.fragmented {
    opacity: 0.5; }
  .reveal .controls .enabled:hover,
  .reveal .controls .enabled.fragmented:hover {
    opacity: 1; }

.reveal:not(.has-vertical-slides) .controls .navigate-left {
  bottom: 1.4em;
  right: 5.5em; }

.reveal:not(.has-vertical-slides) .controls .navigate-right {
  bottom: 1.4em;
  right: 0.5em; }

.reveal:not(.has-horizontal-slides) .controls .navigate-up {
  right: 1.4em;
  bottom: 5em; }

.reveal:not(.has-horizontal-slides) .controls .navigate-down {
  right: 1.4em;
  bottom: 0.5em; }

.reveal.has-dark-background .controls {
  color: #fff; }

.reveal.has-light-background .controls {
  color: #000; }

.reveal.no-hover .controls .controls-arrow:hover:before,
.reveal.no-hover .controls .controls-arrow:active:before {
  -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(45deg);
          transform: translateX(0.5em) translateY(1.55em) rotate(45deg); }

.reveal.no-hover .controls .controls-arrow:hover:after,
.reveal.no-hover .controls .controls-arrow:active:after {
  -webkit-transform: translateX(0.5em) translateY(1.55em) rotate(-45deg);
          transform: translateX(0.5em) translateY(1.55em) rotate(-45deg); }

@media screen and (min-width: 500px) {
  .reveal .controls[data-controls-layout="edges"] {
    top: 0;
    right: 0;
    bottom: 0;
    left: 0; }
  .reveal .controls[data-controls-layout="edges"] .navigate-left,
  .reveal .controls[data-controls-layout="edges"] .navigate-right,
  .reveal .controls[data-controls-layout="edges"] .navigate-up,
  .reveal .controls[data-controls-layout="edges"] .navigate-down {
    bottom: auto;
    right: auto; }
  .reveal .controls[data-controls-layout="edges"] .navigate-left {
    top: 50%;
    left: 8px;
    margin-top: -1.8em; }
  .reveal .controls[data-controls-layout="edges"] .navigate-right {
    top: 50%;
    right: 8px;
    margin-top: -1.8em; }
  .reveal .controls[data-controls-layout="edges"] .navigate-up {
    top: 8px;
    left: 50%;
    margin-left: -1.8em; }
  .reveal .controls[data-controls-layout="edges"] .navigate-down {
    bottom: 8px;
    left: 50%;
    margin-left: -1.8em; } }

/*********************************************
 * PROGRESS BAR
 *********************************************/
.reveal .progress {
  position: absolute;
  display: none;
  height: 3px;
  width: 100%;
  bottom: 0;
  left: 0;
  z-index: 10;
  background-color: rgba(0, 0, 0, 0.2);
  color: #fff; }

.reveal .progress:after {
  content: '';
  display: block;
  position: absolute;
  height: 10px;
  width: 100%;
  top: -10px; }

.reveal .progress span {
  display: block;
  height: 100%;
  width: 0px;
  background-color: currentColor;
  transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }

/*********************************************
 * SLIDE NUMBER
 *********************************************/
.reveal .slide-number {
  position: absolute;
  display: block;
  right: 8px;
  bottom: 8px;
  z-index: 31;
  font-family: Helvetica, sans-serif;
  font-size: 12px;
  line-height: 1;
  color: #fff;
  background-color: rgba(0, 0, 0, 0.4);
  padding: 5px; }

.reveal .slide-number a {
  color: currentColor; }

.reveal .slide-number-delimiter {
  margin: 0 3px; }

/*********************************************
 * SLIDES
 *********************************************/
.reveal {
  position: relative;
  width: 100%;
  height: 100%;
  overflow: hidden;
  -ms-touch-action: none;
      touch-action: none; }

@media only screen and (orientation: landscape) {
  .reveal.ua-iphone {
    position: fixed; } }

.reveal .slides {
  position: absolute;
  width: 100%;
  height: 100%;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  margin: auto;
  pointer-events: none;
  overflow: visible;
  z-index: 1;
  text-align: center;
  -webkit-perspective: 600px;
          perspective: 600px;
  -webkit-perspective-origin: 50% 40%;
          perspective-origin: 50% 40%; }

.reveal .slides > section {
  -ms-perspective: 600px; }

.reveal .slides > section,
.reveal .slides > section > section {
  display: none;
  position: absolute;
  width: 100%;
  padding: 20px 0px;
  pointer-events: auto;
  z-index: 10;
  -webkit-transform-style: flat;
          transform-style: flat;
  transition: -webkit-transform-origin 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985), -webkit-transform 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985), visibility 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985), opacity 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
  transition: transform-origin 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985), transform 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985), visibility 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985), opacity 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }

/* Global transition speed settings */
.reveal[data-transition-speed="fast"] .slides section {
  transition-duration: 400ms; }

.reveal[data-transition-speed="slow"] .slides section {
  transition-duration: 1200ms; }

/* Slide-specific transition speed overrides */
.reveal .slides section[data-transition-speed="fast"] {
  transition-duration: 400ms; }

.reveal .slides section[data-transition-speed="slow"] {
  transition-duration: 1200ms; }

.reveal .slides > section.stack {
  padding-top: 0;
  padding-bottom: 0;
  pointer-events: none; }

.reveal .slides > section.present,
.reveal .slides > section > section.present {
  display: block;
  z-index: 11;
  opacity: 1; }

.reveal .slides > section:empty,
.reveal .slides > section > section:empty,
.reveal .slides > section[data-background-interactive],
.reveal .slides > section > section[data-background-interactive] {
  pointer-events: none; }

.reveal.center,
.reveal.center .slides,
.reveal.center .slides section {
  min-height: 0 !important; }

/* Don't allow interaction with invisible slides */
.reveal .slides > section.future,
.reveal .slides > section > section.future,
.reveal .slides > section.past,
.reveal .slides > section > section.past {
  pointer-events: none; }

.reveal.overview .slides > section,
.reveal.overview .slides > section > section {
  pointer-events: auto; }

.reveal .slides > section.past,
.reveal .slides > section.future,
.reveal .slides > section > section.past,
.reveal .slides > section > section.future {
  opacity: 0; }

/*********************************************
 * Mixins for readability of transitions
 *********************************************/
/*********************************************
 * SLIDE TRANSITION
 * Aliased 'linear' for backwards compatibility
 *********************************************/
.reveal.slide section {
  -webkit-backface-visibility: hidden;
          backface-visibility: hidden; }

.reveal .slides > section[data-transition=slide].past,
.reveal .slides > section[data-transition~=slide-out].past,
.reveal.slide .slides > section:not([data-transition]).past {
  -webkit-transform: translate(-150%, 0);
          transform: translate(-150%, 0); }

.reveal .slides > section[data-transition=slide].future,
.reveal .slides > section[data-transition~=slide-in].future,
.reveal.slide .slides > section:not([data-transition]).future {
  -webkit-transform: translate(150%, 0);
          transform: translate(150%, 0); }

.reveal .slides > section > section[data-transition=slide].past,
.reveal .slides > section > section[data-transition~=slide-out].past,
.reveal.slide .slides > section > section:not([data-transition]).past {
  -webkit-transform: translate(0, -150%);
          transform: translate(0, -150%); }

.reveal .slides > section > section[data-transition=slide].future,
.reveal .slides > section > section[data-transition~=slide-in].future,
.reveal.slide .slides > section > section:not([data-transition]).future {
  -webkit-transform: translate(0, 150%);
          transform: translate(0, 150%); }

.reveal.linear section {
  -webkit-backface-visibility: hidden;
          backface-visibility: hidden; }

.reveal .slides > section[data-transition=linear].past,
.reveal .slides > section[data-transition~=linear-out].past,
.reveal.linear .slides > section:not([data-transition]).past {
  -webkit-transform: translate(-150%, 0);
          transform: translate(-150%, 0); }

.reveal .slides > section[data-transition=linear].future,
.reveal .slides > section[data-transition~=linear-in].future,
.reveal.linear .slides > section:not([data-transition]).future {
  -webkit-transform: translate(150%, 0);
          transform: translate(150%, 0); }

.reveal .slides > section > section[data-transition=linear].past,
.reveal .slides > section > section[data-transition~=linear-out].past,
.reveal.linear .slides > section > section:not([data-transition]).past {
  -webkit-transform: translate(0, -150%);
          transform: translate(0, -150%); }

.reveal .slides > section > section[data-transition=linear].future,
.reveal .slides > section > section[data-transition~=linear-in].future,
.reveal.linear .slides > section > section:not([data-transition]).future {
  -webkit-transform: translate(0, 150%);
          transform: translate(0, 150%); }

/*********************************************
 * CONVEX TRANSITION
 * Aliased 'default' for backwards compatibility
 *********************************************/
.reveal .slides section[data-transition=default].stack,
.reveal.default .slides section.stack {
  -webkit-transform-style: preserve-3d;
          transform-style: preserve-3d; }

.reveal .slides > section[data-transition=default].past,
.reveal .slides > section[data-transition~=default-out].past,
.reveal.default .slides > section:not([data-transition]).past {
  -webkit-transform: translate3d(-100%, 0, 0) rotateY(-90deg) translate3d(-100%, 0, 0);
          transform: translate3d(-100%, 0, 0) rotateY(-90deg) translate3d(-100%, 0, 0); }

.reveal .slides > section[data-transition=default].future,
.reveal .slides > section[data-transition~=default-in].future,
.reveal.default .slides > section:not([data-transition]).future {
  -webkit-transform: translate3d(100%, 0, 0) rotateY(90deg) translate3d(100%, 0, 0);
          transform: translate3d(100%, 0, 0) rotateY(90deg) translate3d(100%, 0, 0); }

.reveal .slides > section > section[data-transition=default].past,
.reveal .slides > section > section[data-transition~=default-out].past,
.reveal.default .slides > section > section:not([data-transition]).past {
  -webkit-transform: translate3d(0, -300px, 0) rotateX(70deg) translate3d(0, -300px, 0);
          transform: translate3d(0, -300px, 0) rotateX(70deg) translate3d(0, -300px, 0); }

.reveal .slides > section > section[data-transition=default].future,
.reveal .slides > section > section[data-transition~=default-in].future,
.reveal.default .slides > section > section:not([data-transition]).future {
  -webkit-transform: translate3d(0, 300px, 0) rotateX(-70deg) translate3d(0, 300px, 0);
          transform: translate3d(0, 300px, 0) rotateX(-70deg) translate3d(0, 300px, 0); }

.reveal .slides section[data-transition=convex].stack,
.reveal.convex .slides section.stack {
  -webkit-transform-style: preserve-3d;
          transform-style: preserve-3d; }

.reveal .slides > section[data-transition=convex].past,
.reveal .slides > section[data-transition~=convex-out].past,
.reveal.convex .slides > section:not([data-transition]).past {
  -webkit-transform: translate3d(-100%, 0, 0) rotateY(-90deg) translate3d(-100%, 0, 0);
          transform: translate3d(-100%, 0, 0) rotateY(-90deg) translate3d(-100%, 0, 0); }

.reveal .slides > section[data-transition=convex].future,
.reveal .slides > section[data-transition~=convex-in].future,
.reveal.convex .slides > section:not([data-transition]).future {
  -webkit-transform: translate3d(100%, 0, 0) rotateY(90deg) translate3d(100%, 0, 0);
          transform: translate3d(100%, 0, 0) rotateY(90deg) translate3d(100%, 0, 0); }

.reveal .slides > section > section[data-transition=convex].past,
.reveal .slides > section > section[data-transition~=convex-out].past,
.reveal.convex .slides > section > section:not([data-transition]).past {
  -webkit-transform: translate3d(0, -300px, 0) rotateX(70deg) translate3d(0, -300px, 0);
          transform: translate3d(0, -300px, 0) rotateX(70deg) translate3d(0, -300px, 0); }

.reveal .slides > section > section[data-transition=convex].future,
.reveal .slides > section > section[data-transition~=convex-in].future,
.reveal.convex .slides > section > section:not([data-transition]).future {
  -webkit-transform: translate3d(0, 300px, 0) rotateX(-70deg) translate3d(0, 300px, 0);
          transform: translate3d(0, 300px, 0) rotateX(-70deg) translate3d(0, 300px, 0); }

/*********************************************
 * CONCAVE TRANSITION
 *********************************************/
.reveal .slides section[data-transition=concave].stack,
.reveal.concave .slides section.stack {
  -webkit-transform-style: preserve-3d;
          transform-style: preserve-3d; }

.reveal .slides > section[data-transition=concave].past,
.reveal .slides > section[data-transition~=concave-out].past,
.reveal.concave .slides > section:not([data-transition]).past {
  -webkit-transform: translate3d(-100%, 0, 0) rotateY(90deg) translate3d(-100%, 0, 0);
          transform: translate3d(-100%, 0, 0) rotateY(90deg) translate3d(-100%, 0, 0); }

.reveal .slides > section[data-transition=concave].future,
.reveal .slides > section[data-transition~=concave-in].future,
.reveal.concave .slides > section:not([data-transition]).future {
  -webkit-transform: translate3d(100%, 0, 0) rotateY(-90deg) translate3d(100%, 0, 0);
          transform: translate3d(100%, 0, 0) rotateY(-90deg) translate3d(100%, 0, 0); }

.reveal .slides > section > section[data-transition=concave].past,
.reveal .slides > section > section[data-transition~=concave-out].past,
.reveal.concave .slides > section > section:not([data-transition]).past {
  -webkit-transform: translate3d(0, -80%, 0) rotateX(-70deg) translate3d(0, -80%, 0);
          transform: translate3d(0, -80%, 0) rotateX(-70deg) translate3d(0, -80%, 0); }

.reveal .slides > section > section[data-transition=concave].future,
.reveal .slides > section > section[data-transition~=concave-in].future,
.reveal.concave .slides > section > section:not([data-transition]).future {
  -webkit-transform: translate3d(0, 80%, 0) rotateX(70deg) translate3d(0, 80%, 0);
          transform: translate3d(0, 80%, 0) rotateX(70deg) translate3d(0, 80%, 0); }

/*********************************************
 * ZOOM TRANSITION
 *********************************************/
.reveal .slides section[data-transition=zoom],
.reveal.zoom .slides section:not([data-transition]) {
  transition-timing-function: ease; }

.reveal .slides > section[data-transition=zoom].past,
.reveal .slides > section[data-transition~=zoom-out].past,
.reveal.zoom .slides > section:not([data-transition]).past {
  visibility: hidden;
  -webkit-transform: scale(16);
          transform: scale(16); }

.reveal .slides > section[data-transition=zoom].future,
.reveal .slides > section[data-transition~=zoom-in].future,
.reveal.zoom .slides > section:not([data-transition]).future {
  visibility: hidden;
  -webkit-transform: scale(0.2);
          transform: scale(0.2); }

.reveal .slides > section > section[data-transition=zoom].past,
.reveal .slides > section > section[data-transition~=zoom-out].past,
.reveal.zoom .slides > section > section:not([data-transition]).past {
  -webkit-transform: translate(0, -150%);
          transform: translate(0, -150%); }

.reveal .slides > section > section[data-transition=zoom].future,
.reveal .slides > section > section[data-transition~=zoom-in].future,
.reveal.zoom .slides > section > section:not([data-transition]).future {
  -webkit-transform: translate(0, 150%);
          transform: translate(0, 150%); }

/*********************************************
 * CUBE TRANSITION
 *
 * WARNING:
 * this is deprecated and will be removed in a
 * future version.
 *********************************************/
.reveal.cube .slides {
  -webkit-perspective: 1300px;
          perspective: 1300px; }

.reveal.cube .slides section {
  padding: 30px;
  min-height: 700px;
  -webkit-backface-visibility: hidden;
          backface-visibility: hidden;
  box-sizing: border-box;
  -webkit-transform-style: preserve-3d;
          transform-style: preserve-3d; }

.reveal.center.cube .slides section {
  min-height: 0; }

.reveal.cube .slides section:not(.stack):before {
  content: '';
  position: absolute;
  display: block;
  width: 100%;
  height: 100%;
  left: 0;
  top: 0;
  background: rgba(0, 0, 0, 0.1);
  border-radius: 4px;
  -webkit-transform: translateZ(-20px);
          transform: translateZ(-20px); }

.reveal.cube .slides section:not(.stack):after {
  content: '';
  position: absolute;
  display: block;
  width: 90%;
  height: 30px;
  left: 5%;
  bottom: 0;
  background: none;
  z-index: 1;
  border-radius: 4px;
  box-shadow: 0px 95px 25px rgba(0, 0, 0, 0.2);
  -webkit-transform: translateZ(-90px) rotateX(65deg);
          transform: translateZ(-90px) rotateX(65deg); }

.reveal.cube .slides > section.stack {
  padding: 0;
  background: none; }

.reveal.cube .slides > section.past {
  -webkit-transform-origin: 100% 0%;
          transform-origin: 100% 0%;
  -webkit-transform: translate3d(-100%, 0, 0) rotateY(-90deg);
          transform: translate3d(-100%, 0, 0) rotateY(-90deg); }

.reveal.cube .slides > section.future {
  -webkit-transform-origin: 0% 0%;
          transform-origin: 0% 0%;
  -webkit-transform: translate3d(100%, 0, 0) rotateY(90deg);
          transform: translate3d(100%, 0, 0) rotateY(90deg); }

.reveal.cube .slides > section > section.past {
  -webkit-transform-origin: 0% 100%;
          transform-origin: 0% 100%;
  -webkit-transform: translate3d(0, -100%, 0) rotateX(90deg);
          transform: translate3d(0, -100%, 0) rotateX(90deg); }

.reveal.cube .slides > section > section.future {
  -webkit-transform-origin: 0% 0%;
          transform-origin: 0% 0%;
  -webkit-transform: translate3d(0, 100%, 0) rotateX(-90deg);
          transform: translate3d(0, 100%, 0) rotateX(-90deg); }

/*********************************************
 * PAGE TRANSITION
 *
 * WARNING:
 * this is deprecated and will be removed in a
 * future version.
 *********************************************/
.reveal.page .slides {
  -webkit-perspective-origin: 0% 50%;
          perspective-origin: 0% 50%;
  -webkit-perspective: 3000px;
          perspective: 3000px; }

.reveal.page .slides section {
  padding: 30px;
  min-height: 700px;
  box-sizing: border-box;
  -webkit-transform-style: preserve-3d;
          transform-style: preserve-3d; }

.reveal.page .slides section.past {
  z-index: 12; }

.reveal.page .slides section:not(.stack):before {
  content: '';
  position: absolute;
  display: block;
  width: 100%;
  height: 100%;
  left: 0;
  top: 0;
  background: rgba(0, 0, 0, 0.1);
  -webkit-transform: translateZ(-20px);
          transform: translateZ(-20px); }

.reveal.page .slides section:not(.stack):after {
  content: '';
  position: absolute;
  display: block;
  width: 90%;
  height: 30px;
  left: 5%;
  bottom: 0;
  background: none;
  z-index: 1;
  border-radius: 4px;
  box-shadow: 0px 95px 25px rgba(0, 0, 0, 0.2);
  -webkit-transform: translateZ(-90px) rotateX(65deg); }

.reveal.page .slides > section.stack {
  padding: 0;
  background: none; }

.reveal.page .slides > section.past {
  -webkit-transform-origin: 0% 0%;
          transform-origin: 0% 0%;
  -webkit-transform: translate3d(-40%, 0, 0) rotateY(-80deg);
          transform: translate3d(-40%, 0, 0) rotateY(-80deg); }

.reveal.page .slides > section.future {
  -webkit-transform-origin: 100% 0%;
          transform-origin: 100% 0%;
  -webkit-transform: translate3d(0, 0, 0);
          transform: translate3d(0, 0, 0); }

.reveal.page .slides > section > section.past {
  -webkit-transform-origin: 0% 0%;
          transform-origin: 0% 0%;
  -webkit-transform: translate3d(0, -40%, 0) rotateX(80deg);
          transform: translate3d(0, -40%, 0) rotateX(80deg); }

.reveal.page .slides > section > section.future {
  -webkit-transform-origin: 0% 100%;
          transform-origin: 0% 100%;
  -webkit-transform: translate3d(0, 0, 0);
          transform: translate3d(0, 0, 0); }

/*********************************************
 * FADE TRANSITION
 *********************************************/
.reveal .slides section[data-transition=fade],
.reveal.fade .slides section:not([data-transition]),
.reveal.fade .slides > section > section:not([data-transition]) {
  -webkit-transform: none;
          transform: none;
  transition: opacity 0.5s; }

.reveal.fade.overview .slides section,
.reveal.fade.overview .slides > section > section {
  transition: none; }

/*********************************************
 * NO TRANSITION
 *********************************************/
.reveal .slides section[data-transition=none],
.reveal.none .slides section:not([data-transition]) {
  -webkit-transform: none;
          transform: none;
  transition: none; }

/*********************************************
 * PAUSED MODE
 *********************************************/
.reveal .pause-overlay {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;
  background: black;
  visibility: hidden;
  opacity: 0;
  z-index: 100;
  transition: all 1s ease; }

.reveal .pause-overlay .resume-button {
  position: absolute;
  bottom: 20px;
  right: 20px;
  color: #ccc;
  border-radius: 2px;
  padding: 6px 14px;
  border: 2px solid #ccc;
  font-size: 16px;
  background: transparent;
  cursor: pointer; }
  .reveal .pause-overlay .resume-button:hover {
    color: #fff;
    border-color: #fff; }

.reveal.paused .pause-overlay {
  visibility: visible;
  opacity: 1; }

/*********************************************
 * FALLBACK
 *********************************************/
.no-transforms {
  overflow-y: auto; }

.no-transforms .reveal .slides {
  position: relative;
  width: 80%;
  height: auto !important;
  top: 0;
  left: 50%;
  margin: 0;
  text-align: center; }

.no-transforms .reveal .controls,
.no-transforms .reveal .progress {
  display: none !important; }

.no-transforms .reveal .slides section {
  display: block !important;
  opacity: 1 !important;
  position: relative !important;
  height: auto;
  min-height: 0;
  top: 0;
  left: -50%;
  margin: 70px 0;
  -webkit-transform: none;
          transform: none; }

.no-transforms .reveal .slides section section {
  left: 0; }

.reveal .no-transition,
.reveal .no-transition * {
  transition: none !important; }

/*********************************************
 * PER-SLIDE BACKGROUNDS
 *********************************************/
.reveal .backgrounds {
  position: absolute;
  width: 100%;
  height: 100%;
  top: 0;
  left: 0;
  -webkit-perspective: 600px;
          perspective: 600px; }

.reveal .slide-background {
  display: none;
  position: absolute;
  width: 100%;
  height: 100%;
  opacity: 0;
  visibility: hidden;
  overflow: hidden;
  background-color: transparent;
  transition: all 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }

.reveal .slide-background-content {
  position: absolute;
  width: 100%;
  height: 100%;
  background-position: 50% 50%;
  background-repeat: no-repeat;
  background-size: cover; }

.reveal .slide-background.stack {
  display: block; }

.reveal .slide-background.present {
  opacity: 1;
  visibility: visible;
  z-index: 2; }

.print-pdf .reveal .slide-background {
  opacity: 1 !important;
  visibility: visible !important; }

/* Video backgrounds */
.reveal .slide-background video {
  position: absolute;
  width: 100%;
  height: 100%;
  max-width: none;
  max-height: none;
  top: 0;
  left: 0;
  -o-object-fit: cover;
     object-fit: cover; }

.reveal .slide-background[data-background-size="contain"] video {
  -o-object-fit: contain;
     object-fit: contain; }

/* Immediate transition style */
.reveal[data-background-transition=none] > .backgrounds .slide-background,
.reveal > .backgrounds .slide-background[data-background-transition=none] {
  transition: none; }

/* Slide */
.reveal[data-background-transition=slide] > .backgrounds .slide-background,
.reveal > .backgrounds .slide-background[data-background-transition=slide] {
  opacity: 1;
  -webkit-backface-visibility: hidden;
          backface-visibility: hidden; }

.reveal[data-background-transition=slide] > .backgrounds .slide-background.past,
.reveal > .backgrounds .slide-background.past[data-background-transition=slide] {
  -webkit-transform: translate(-100%, 0);
          transform: translate(-100%, 0); }

.reveal[data-background-transition=slide] > .backgrounds .slide-background.future,
.reveal > .backgrounds .slide-background.future[data-background-transition=slide] {
  -webkit-transform: translate(100%, 0);
          transform: translate(100%, 0); }

.reveal[data-background-transition=slide] > .backgrounds .slide-background > .slide-background.past,
.reveal > .backgrounds .slide-background > .slide-background.past[data-background-transition=slide] {
  -webkit-transform: translate(0, -100%);
          transform: translate(0, -100%); }

.reveal[data-background-transition=slide] > .backgrounds .slide-background > .slide-background.future,
.reveal > .backgrounds .slide-background > .slide-background.future[data-background-transition=slide] {
  -webkit-transform: translate(0, 100%);
          transform: translate(0, 100%); }

/* Convex */
.reveal[data-background-transition=convex] > .backgrounds .slide-background.past,
.reveal > .backgrounds .slide-background.past[data-background-transition=convex] {
  opacity: 0;
  -webkit-transform: translate3d(-100%, 0, 0) rotateY(-90deg) translate3d(-100%, 0, 0);
          transform: translate3d(-100%, 0, 0) rotateY(-90deg) translate3d(-100%, 0, 0); }

.reveal[data-background-transition=convex] > .backgrounds .slide-background.future,
.reveal > .backgrounds .slide-background.future[data-background-transition=convex] {
  opacity: 0;
  -webkit-transform: translate3d(100%, 0, 0) rotateY(90deg) translate3d(100%, 0, 0);
          transform: translate3d(100%, 0, 0) rotateY(90deg) translate3d(100%, 0, 0); }

.reveal[data-background-transition=convex] > .backgrounds .slide-background > .slide-background.past,
.reveal > .backgrounds .slide-background > .slide-background.past[data-background-transition=convex] {
  opacity: 0;
  -webkit-transform: translate3d(0, -100%, 0) rotateX(90deg) translate3d(0, -100%, 0);
          transform: translate3d(0, -100%, 0) rotateX(90deg) translate3d(0, -100%, 0); }

.reveal[data-background-transition=convex] > .backgrounds .slide-background > .slide-background.future,
.reveal > .backgrounds .slide-background > .slide-background.future[data-background-transition=convex] {
  opacity: 0;
  -webkit-transform: translate3d(0, 100%, 0) rotateX(-90deg) translate3d(0, 100%, 0);
          transform: translate3d(0, 100%, 0) rotateX(-90deg) translate3d(0, 100%, 0); }

/* Concave */
.reveal[data-background-transition=concave] > .backgrounds .slide-background.past,
.reveal > .backgrounds .slide-background.past[data-background-transition=concave] {
  opacity: 0;
  -webkit-transform: translate3d(-100%, 0, 0) rotateY(90deg) translate3d(-100%, 0, 0);
          transform: translate3d(-100%, 0, 0) rotateY(90deg) translate3d(-100%, 0, 0); }

.reveal[data-background-transition=concave] > .backgrounds .slide-background.future,
.reveal > .backgrounds .slide-background.future[data-background-transition=concave] {
  opacity: 0;
  -webkit-transform: translate3d(100%, 0, 0) rotateY(-90deg) translate3d(100%, 0, 0);
          transform: translate3d(100%, 0, 0) rotateY(-90deg) translate3d(100%, 0, 0); }

.reveal[data-background-transition=concave] > .backgrounds .slide-background > .slide-background.past,
.reveal > .backgrounds .slide-background > .slide-background.past[data-background-transition=concave] {
  opacity: 0;
  -webkit-transform: translate3d(0, -100%, 0) rotateX(-90deg) translate3d(0, -100%, 0);
          transform: translate3d(0, -100%, 0) rotateX(-90deg) translate3d(0, -100%, 0); }

.reveal[data-background-transition=concave] > .backgrounds .slide-background > .slide-background.future,
.reveal > .backgrounds .slide-background > .slide-background.future[data-background-transition=concave] {
  opacity: 0;
  -webkit-transform: translate3d(0, 100%, 0) rotateX(90deg) translate3d(0, 100%, 0);
          transform: translate3d(0, 100%, 0) rotateX(90deg) translate3d(0, 100%, 0); }

/* Zoom */
.reveal[data-background-transition=zoom] > .backgrounds .slide-background,
.reveal > .backgrounds .slide-background[data-background-transition=zoom] {
  transition-timing-function: ease; }

.reveal[data-background-transition=zoom] > .backgrounds .slide-background.past,
.reveal > .backgrounds .slide-background.past[data-background-transition=zoom] {
  opacity: 0;
  visibility: hidden;
  -webkit-transform: scale(16);
          transform: scale(16); }

.reveal[data-background-transition=zoom] > .backgrounds .slide-background.future,
.reveal > .backgrounds .slide-background.future[data-background-transition=zoom] {
  opacity: 0;
  visibility: hidden;
  -webkit-transform: scale(0.2);
          transform: scale(0.2); }

.reveal[data-background-transition=zoom] > .backgrounds .slide-background > .slide-background.past,
.reveal > .backgrounds .slide-background > .slide-background.past[data-background-transition=zoom] {
  opacity: 0;
  visibility: hidden;
  -webkit-transform: scale(16);
          transform: scale(16); }

.reveal[data-background-transition=zoom] > .backgrounds .slide-background > .slide-background.future,
.reveal > .backgrounds .slide-background > .slide-background.future[data-background-transition=zoom] {
  opacity: 0;
  visibility: hidden;
  -webkit-transform: scale(0.2);
          transform: scale(0.2); }

/* Global transition speed settings */
.reveal[data-transition-speed="fast"] > .backgrounds .slide-background {
  transition-duration: 400ms; }

.reveal[data-transition-speed="slow"] > .backgrounds .slide-background {
  transition-duration: 1200ms; }

/*********************************************
 * OVERVIEW
 *********************************************/
.reveal.overview {
  -webkit-perspective-origin: 50% 50%;
          perspective-origin: 50% 50%;
  -webkit-perspective: 700px;
          perspective: 700px; }
  .reveal.overview .slides {
    -moz-transform-style: preserve-3d; }
  .reveal.overview .slides section {
    height: 100%;
    top: 0 !important;
    opacity: 1 !important;
    overflow: hidden;
    visibility: visible !important;
    cursor: pointer;
    box-sizing: border-box; }
  .reveal.overview .slides section:hover,
  .reveal.overview .slides section.present {
    outline: 10px solid rgba(150, 150, 150, 0.4);
    outline-offset: 10px; }
  .reveal.overview .slides section .fragment {
    opacity: 1;
    transition: none; }
  .reveal.overview .slides section:after,
  .reveal.overview .slides section:before {
    display: none !important; }
  .reveal.overview .slides > section.stack {
    padding: 0;
    top: 0 !important;
    background: none;
    outline: none;
    overflow: visible; }
  .reveal.overview .backgrounds {
    -webkit-perspective: inherit;
            perspective: inherit;
    -moz-transform-style: preserve-3d; }
  .reveal.overview .backgrounds .slide-background {
    opacity: 1;
    visibility: visible;
    outline: 10px solid rgba(150, 150, 150, 0.1);
    outline-offset: 10px; }
  .reveal.overview .backgrounds .slide-background.stack {
    overflow: visible; }

.reveal.overview .slides section,
.reveal.overview-deactivating .slides section {
  transition: none; }

.reveal.overview .backgrounds .slide-background,
.reveal.overview-deactivating .backgrounds .slide-background {
  transition: none; }

/*********************************************
 * RTL SUPPORT
 *********************************************/
.reveal.rtl .slides,
.reveal.rtl .slides h1,
.reveal.rtl .slides h2,
.reveal.rtl .slides h3,
.reveal.rtl .slides h4,
.reveal.rtl .slides h5,
.reveal.rtl .slides h6 {
  direction: rtl;
  font-family: sans-serif; }

.reveal.rtl pre,
.reveal.rtl code {
  direction: ltr; }

.reveal.rtl ol,
.reveal.rtl ul {
  text-align: right; }

.reveal.rtl .progress span {
  float: right; }

/*********************************************
 * PARALLAX BACKGROUND
 *********************************************/
.reveal.has-parallax-background .backgrounds {
  transition: all 0.8s ease; }

/* Global transition speed settings */
.reveal.has-parallax-background[data-transition-speed="fast"] .backgrounds {
  transition-duration: 400ms; }

.reveal.has-parallax-background[data-transition-speed="slow"] .backgrounds {
  transition-duration: 1200ms; }

/*********************************************
 * LINK PREVIEW OVERLAY
 *********************************************/
.reveal .overlay {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;
  z-index: 1000;
  background: rgba(0, 0, 0, 0.9);
  opacity: 0;
  visibility: hidden;
  transition: all 0.3s ease; }

.reveal .overlay.visible {
  opacity: 1;
  visibility: visible; }

.reveal .overlay .spinner {
  position: absolute;
  display: block;
  top: 50%;
  left: 50%;
  width: 32px;
  height: 32px;
  margin: -16px 0 0 -16px;
  z-index: 10;
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    <body for="html-export" data-presentation-mode>
      <div class="mume markdown-preview  " data-presentation-mode>
      
    <div style="display:none;"><link rel="stylesheet" href="../common/css/zhangt-style.css">
<link rel="stylesheet" href="../common/css/font-awesome-4.7.0/css/font-awesome.css">
</div>
    <div class="reveal">
      <div class="slides">
        <section data-notes lineno="10" class="slide " data-line="10" data-h="0" data-v="0">
<div id="logo">
    <img src="../common/img/xiaohui.png" style height="120px">
    <img src="../common/img/bdts.png" style="margin-top:0.5rem" height="100px">
</div>
<div>
    <h1 style="width: 50%">
        &#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;<br> 
        <span style="font-size: 0.6em">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</span>
    </h1>
    <h2>&#x5F20;&#x817E;</h2>
    <h3>tengzhang@hust.edu.cn</h3>
</div>
</section><section><section data-notes lineno="25" class="slide " data-line="25" data-h="1" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x56FE;&#x662F;&#x4E00;&#x79CD;&#x5E38;&#x89C1;&#x7684;&#x6570;&#x636E;&#x7ED3;&#x6784;&#xFF0C;&#x7531;&#x4E00;&#x7EC4;&#x70B9;&#x96C6;&#x548C;&#x4E00;&#x7EC4;&#x8FB9;&#x96C6;&#x6784;&#x6210;</p>
<ul>
<li>&#x76F8;&#x6BD4;&#x4E8E;&#x5355;&#x7EAF;&#x7684;&#x70B9;&#x96C6;&#xFF0C;&#x56FE;&#x4E2D;&#x7684;&#x8FB9;&#x53EF;&#x4EE5;&#x63CF;&#x8FF0;&#x7269;&#x4F53;&#x95F4;&#x7684;&#x590D;&#x6742;&#x5173;&#x7CFB;</li>
</ul>
<br>
<p>&#x56FE;&#x662F;&#x4E00;&#x79CD;&#x63CF;&#x8FF0;&#x590D;&#x6742;&#x7CFB;&#x7EDF;&#x7684;&#x901A;&#x7528;&#x8BED;&#x8A00;</p>
<ul>
<li>&#x793E;&#x4EA4;&#x7F51;&#x7EDC;</li>
<li>&#x8BBA;&#x6587;&#x5F15;&#x7528;</li>
<li>&#x4EA4;&#x901A;&#x8DEF;&#x7F51;</li>
<li>&#x77E5;&#x8BC6;&#x56FE;&#x8C31;</li>
<li>&#x901A;&#x4FE1;&#x7F51;&#x7EDC;</li>
<li>&#x5206;&#x5B50;&#x7ED3;&#x6784;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="58" class="slide " data-line="58" data-h="1" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x7B26;&#x53F7;&#x8868;&#x793A;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x7ED9;&#x5B9A;&#x70B9;&#x96C6;<span class="mathjax-exps">$\Vcal$</span>&#x548C;&#x8FD9;&#x4E9B;&#x70B9;&#x95F4;&#x7684;&#x8FB9;&#x96C6;<span class="mathjax-exps">$\Ecal$</span>&#x5C31;&#x6784;&#x6210;&#x4E86;&#x56FE;<span class="mathjax-exps">$\Gcal = (\Vcal, \Ecal)$</span></p>
<br>
<p>&#x5BF9;&#x4E8E;&#x70B9;<span class="mathjax-exps">$u, v \in \Vcal$</span></p>
<ul>
<li>&#x82E5;&#x5176;&#x5B58;&#x5728;&#x8FDE;&#x8FB9;(&#x5173;&#x7CFB;)&#xFF0C;&#x5219;&#x8BB0;<span class="mathjax-exps">$(u,v) \in \Ecal$</span></li>
<li>&#x82E5;&#x8FB9;&#x6CA1;&#x6709;&#x65B9;&#x5411;&#xFF0C;&#x5219;<span class="mathjax-exps">$(u,v) \in \Ecal \Longleftrightarrow (v,u) \in \Ecal$</span></li>
</ul>
<br>
<p>&#x90BB;&#x63A5;&#x77E9;&#x9635;<span class="mathjax-exps">$\Av \in \Rbb^{|\Vcal| \times |\Vcal|}$</span></p>
<ul>
<li>&#x82E5;&#x8FB9;&#x6CA1;&#x6709;&#x6743;&#x91CD;&#xFF0C;<span class="mathjax-exps">$[\Av]_{uv} = 1_{(u,v) \in \Ecal}$</span>&#xFF1B;&#x82E5;&#x8FB9;&#x4E0A;&#x6709;&#x6743;&#x91CD;&#xFF0C;<span class="mathjax-exps">$[\Av]_{uv}$</span>&#x5C31;&#x7B49;&#x4E8E;<span class="mathjax-exps">$(u,v)$</span>&#x7684;&#x6743;&#x91CD;</li>
<li>&#x82E5;&#x8FB9;&#x6CA1;&#x6709;&#x65B9;&#x5411;&#xFF0C;&#x5219;<span class="mathjax-exps">$\Av$</span>&#x662F;<span class="blue">&#x5BF9;&#x79F0;</span>&#x77E9;&#x9635;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="92" class="slide " data-line="92" data-h="1" data-v="2">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x591A;&#x91CD;&#x5173;&#x7CFB;&#x56FE;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5173;&#x7CFB;&#x5206;&#x79CD;&#x7C7B;&#xFF0C;&#x5F15;&#x5165;&#x5173;&#x7CFB;&#x96C6;&#x5408;<span class="mathjax-exps">$\Rcal$</span></p>
<ul>
<li>&#x8FB9;&#x7684;&#x8868;&#x793A;&#xFF1A;<span class="mathjax-exps">$(u, \tau, v) \in \Ecal$</span>&#xFF0C;&#x70B9;<span class="mathjax-exps">$u$</span>&#x3001;<span class="mathjax-exps">$v$</span>&#x95F4;&#x6709;&#x5173;&#x7CFB;<span class="mathjax-exps">$\tau$</span></li>
<li>&#x90BB;&#x63A5;&#x5F20;&#x91CF;<span class="mathjax-exps">$\Av \in \Rbb^{|\Vcal| \times |\Rcal| \times |\Vcal|}$</span></li>
</ul>
<br>
<p><span class="blue">&#x5F02;&#x8D28;&#x56FE;</span>&#xFF1A;&#x70B9;&#x4E5F;&#x5206;&#x79CD;&#x7C7B;&#xFF0C;&#x5373;&#x70B9;&#x96C6;<span class="mathjax-exps">$\Vcal$</span>&#x53EF;&#x4EE5;&#x5212;&#x5206;&#x6210;<span class="mathjax-exps">$k$</span>&#x4E2A;&#x5B50;&#x96C6;<span class="mathjax-exps">$\Vcal = \Vcal_1 \cup \Vcal_2 \cup \cdots \cup \Vcal_k$</span></p>
<ul>
<li>&#x4E09;&#x7C7B;&#x70B9;&#xFF1A;&#x86CB;&#x767D;&#x8D28;&#x3001;&#x836F;&#x7269;&#x3001;&#x75BE;&#x75C5;&#xFF0C;&#x524D;&#x4E24;&#x7C7B;&#x70B9;&#x95F4;&#xFF1A;&#x6709;&#x836F;&#x6548;&#xFF0C;&#x540E;&#x4E24;&#x7C7B;&#x70B9;&#x95F4;&#xFF1A;&#x6CBB;&#x6108;</li>
<li>&#x591A;&#x90E8;&#x56FE;(multipartite graphs)&#x662F;&#x5F02;&#x8D28;&#x56FE;&#x7684;&#x7ECF;&#x5178;&#x4F8B;&#x5B50;</li>
</ul>
<br>
<p><span class="blue">&#x591A;&#x91CD;&#x56FE;</span>&#xFF1A;&#x56FE;&#x5206;&#x591A;&#x5C42;&#xFF0C;&#x6BCF;&#x5C42;&#x540C;&#x70B9;&#x5F02;&#x8FB9;&#xFF0C;&#x540C;&#x4E00;&#x5C42;&#x7684;&#x8FB9;&#x8868;&#x793A;&#x540C;&#x4E00;&#x79CD;&#x5173;&#x7CFB;</p>
<ul>
<li>&#x70B9;&#x4EE3;&#x8868;&#x57CE;&#x5E02;&#xFF0C;&#x5C42;&#x4EE3;&#x8868;&#x67D0;&#x79CD;&#x4EA4;&#x901A;&#x65B9;&#x5F0F;&#xFF0C;&#x5982;&#x6C7D;&#x8F66;&#x3001;&#x9AD8;&#x94C1;&#x3001;&#x98DE;&#x673A;&#x3001;&#x8F6E;&#x8239;&#x7B49;</li>
<li>&#x4E0D;&#x540C;&#x5C42;&#x7684;&#x540C;&#x4E00;&#x4E2A;&#x70B9;&#x4E5F;&#x53EF;&#x4EE5;&#x8FDE;&#x8FB9;&#xFF0C;&#x8868;&#x793A;&#x53EF;&#x4EE5;&#x4ECE;&#x4E00;&#x79CD;&#x4EA4;&#x901A;&#x65B9;&#x5F0F;&#x5207;&#x6362;&#x5230;&#x53E6;&#x4E00;&#x79CD;&#x4EA4;&#x901A;&#x65B9;&#x5F0F;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="129" class="slide " data-line="129" data-h="1" data-v="3">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x5C5E;&#x6027;&#x4FE1;&#x606F;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x70B9;&#x53EF;&#x4EE5;&#x6709;&#x7279;&#x5F81;&#x4FE1;&#x606F;</p>
<ul>
<li>&#x793E;&#x4EA4;&#x7F51;&#x7EDC;&#x4E2D;&#x70B9;&#x7684;&#x7279;&#x5F81;&#x662F;&#x6BCF;&#x4E2A;&#x7528;&#x6237;&#x7684;&#x4E2A;&#x4EBA;&#x4FE1;&#x606F;</li>
<li>&#x4EA4;&#x901A;&#x8DEF;&#x7F51;&#x4E2D;&#x70B9;&#x7684;&#x7279;&#x5F81;&#x662F;&#x6BCF;&#x4E2A;&#x8DEF;&#x53E3;&#x7684;&#x6D41;&#x91CF;&#x4FE1;&#x606F;</li>
</ul>
<br>
<p>&#x8FB9;&#x9664;&#x4E86;&#x53EF;&#x4EE5;&#x6709;&#x79BB;&#x6563;&#x7684;&#x79CD;&#x7C7B;&#xFF0C;&#x4E5F;&#x53EF;&#x4EE5;&#x6709;&#x7279;&#x5F81;</p>
<br>
<p>&#x751A;&#x81F3;&#x6574;&#x56FE;&#x4E5F;&#x53EF;&#x4EE5;&#x6709;</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="160" class="slide " data-line="160" data-h="1" data-v="4">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE; vs. &#x7F51;&#x7EDC;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x4E24;&#x8005;&#x5927;&#x591A;&#x6570;&#x65F6;&#x5019;&#x662F;&#x4E00;&#x4E2A;&#x610F;&#x601D;&#xFF0C;&#x66F4;&#x591A;&#x7684;&#x533A;&#x522B;&#x5728;&#x4E8E;&#x6587;&#x5316;&#x5708;&#x5B50;</p>
<ul>
<li>&#x56FE;&#x591A;&#x7528;&#x4E8E;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x5708;&#x5B50;</li>
<li>&#x7F51;&#x7EDC;&#x591A;&#x7528;&#x4E8E;&#x6570;&#x636E;&#x6316;&#x6398;&#x3001;&#x7F51;&#x7EDC;&#x5206;&#x6790;&#x7B49;&#x4E0B;&#x6E38;&#x5708;&#x5B50;</li>
</ul>
<br>
<p>&#x5728;&#x672C;&#x8BFE;&#x7A0B;&#x4E2D;</p>
<ul>
<li>&#x7528;&#x56FE;&#x8868;&#x793A;&#x62BD;&#x8C61;&#x7684;&#x6570;&#x636E;&#x7ED3;&#x6784;</li>
<li>&#x7528;&#x7F51;&#x7EDC;&#x8868;&#x793A;&#x5177;&#x4F53;&#x7684;&#x73B0;&#x5B9E;&#x6570;&#x636E;&#xFF0C;&#x4F8B;&#x5982;&#x793E;&#x4EA4;&#x7F51;&#x7EDC;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="190" class="slide " data-line="190" data-h="2" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE;&#x4E0A;&#x7684;&#x5B66;&#x4E60;&#x4EFB;&#x52A1;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p><span class="blue">&#x70B9;&#x5206;&#x7C7B;</span></p>
<ul>
<li>&#x8F93;&#x5165;&#xFF1A;&#x70B9;&#x96C6;&#x7684;&#x4E00;&#x4E2A;&#x5C0F;&#x5B50;&#x96C6;&#x6709;&#x7C7B;&#x522B;&#x6807;&#x8BB0;&#x7684;&#x56FE;</li>
<li>&#x76EE;&#x6807;&#xFF1A;&#x9884;&#x6D4B;&#x5176;&#x4ED6;&#x672A;&#x6807;&#x8BB0;&#x70B9;&#x7684;&#x7C7B;&#x522B;</li>
</ul>
<br>
<p>&#x4F8B;&#x5B50;</p>
<ul>
<li>&#x793E;&#x4EA4;&#x7F51;&#x7EDC;&#x4E2D;&#x673A;&#x5668;&#x4EBA;&#x7528;&#x6237;&#x68C0;&#x6D4B;</li>
<li>&#x5206;&#x5B50;&#x7ED3;&#x6784;&#x4E2D;&#x9884;&#x6D4B;&#x8282;&#x70B9;&#x86CB;&#x767D;&#x8D28;&#x7684;&#x529F;&#x80FD;</li>
<li>&#x8BBA;&#x6587;&#x5F15;&#x7528;&#x7F51;&#x7EDC;&#x4E2D;&#x7684;&#x6587;&#x6863;&#x4E3B;&#x9898;&#x5206;&#x7C7B;</li>
</ul>
<br>
<p>&#x7279;&#x70B9;</p>
<ul>
<li>&#x4E0E;&#x4F20;&#x7EDF;&#x7684;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4E0D;&#x540C;&#xFF0C;&#x6837;&#x672C;&#x4E0D;&#x662F;&#x72EC;&#x7ACB;&#x540C;&#x5206;&#x5E03;&#x7684;</li>
<li>&#x5229;&#x7528;&#x540C;&#x8D28;&#x6027;&#xFF0C;&#x76F8;&#x90BB;&#x70B9;&#x62E5;&#x6709;&#x6BD4;&#x8F83;&#x63A5;&#x8FD1;&#x7684;&#x7279;&#x5F81;</li>
<li>&#x5229;&#x7528;&#x7ED3;&#x6784;&#x7B49;&#x4EF7;&#x6027;&#xFF0C;&#x62E5;&#x6709;&#x76F8;&#x4F3C;&#x90BB;&#x5C45;&#x7ED3;&#x6784;&#x7684;&#x70B9;&#x5F80;&#x5F80;&#x6709;&#x76F8;&#x4F3C;&#x7684;&#x7C7B;&#x522B;&#x6807;&#x8BB0;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="229" class="slide " data-line="229" data-h="2" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE;&#x4E0A;&#x7684;&#x5B66;&#x4E60;&#x4EFB;&#x52A1;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p><span class="blue">&#x5173;&#x7CFB;&#x9884;&#x6D4B;</span>&#xFF0C;&#x4E5F;&#x53EB;&#x94FE;&#x63A5;&#x9884;&#x6D4B;&#x3001;&#x56FE;&#x8865;&#x5168;&#x3001;&#x5173;&#x7CFB;&#x63A8;&#x7406;</p>
<ul>
<li>&#x8F93;&#x5165;&#xFF1A;<span class="mathjax-exps">$\Vcal$</span>&#xFF0C;<span class="mathjax-exps">$\Ecal_{train}$</span></li>
<li>&#x76EE;&#x6807;&#xFF1A;&#x9884;&#x6D4B;<span class="mathjax-exps">$\Ecal \setminus \Ecal_{train}$</span></li>
</ul>
<br>
<p>&#x4F8B;&#x5B50;</p>
<ul>
<li>&#x793E;&#x4EA4;&#x5E73;&#x53F0;&#x4E0A;&#x7684;&#x63A8;&#x8350;</li>
<li>&#x751F;&#x7269;&#x533B;&#x5B66;&#x4E2D;&#x9884;&#x6D4B;&#x836F;&#x6548;</li>
</ul>
<br>
<p>&#x4EFB;&#x52A1;&#x7684;&#x96BE;&#x5EA6;&#x53D6;&#x51B3;&#x4E8E;&#x56FE;&#x7684;&#x7C7B;&#x578B;</p>
<ul>
<li>&#x793E;&#x4EA4;&#x7F51;&#x7EDC;&#x4E2D;&#x53EA;&#x6709;&#x201C;&#x670B;&#x53CB;&#x201D;&#x4E00;&#x79CD;&#x5173;&#x7CFB;&#x5C31;&#x5F88;&#x7B80;&#x5355;&#xFF0C;&#x6BD4;&#x5982;&#x53EA;&#x770B;&#x8FD9;&#x4E24;&#x4E2A;&#x70B9;&#x6709;&#x591A;&#x5C11;&#x5171;&#x540C;&#x597D;&#x53CB;</li>
<li>&#x751F;&#x7269;&#x533B;&#x5B66;&#x4E2D;&#x6709;&#x51E0;&#x767E;&#x79CD;&#x5173;&#x7CFB;&#xFF0C;&#x9884;&#x6D4B;&#x5C31;&#x5F88;&#x96BE;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="266" class="slide " data-line="266" data-h="2" data-v="2">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE;&#x4E0A;&#x7684;&#x5B66;&#x4E60;&#x4EFB;&#x52A1;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p><span class="blue">&#x793E;&#x533A;&#x53D1;&#x73B0;</span></p>
<ul>
<li>&#x70B9;&#x5206;&#x7C7B;&#x548C;&#x8FB9;&#x9884;&#x6D4B;&#x7C7B;&#x4F3C;&#x4E8E;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4E2D;&#x7684;&#x76D1;&#x7763;&#x5B66;&#x4E60;</li>
<li>&#x793E;&#x533A;&#x53D1;&#x73B0;&#x7C7B;&#x4F3C;&#x4E8E;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4E2D;&#x7684;&#x65E0;&#x76D1;&#x7763;&#x5B66;&#x4E60;&#xFF1A;&#x805A;&#x7C7B;</li>
</ul>
<p>&#x4F8B;&#x5982;&#x7528;&#x8C37;&#x6B4C;&#x5B66;&#x672F;&#x7684;&#x4FE1;&#x606F;&#x5EFA;&#x7ACB;&#x4E00;&#x4E2A;&#x8BBA;&#x6587;&#x5408;&#x4F5C;&#x7F51;&#x7EDC;&#xFF0C;&#x4E24;&#x4E2A;&#x70B9;&#x6709;&#x8FB9;&#x76F8;&#x90BB;&#x4EE3;&#x8868;&#x8FD9;&#x4E24;&#x4F4D;&#x4F5C;&#x8005;&#x5408;&#x4F5C;&#x8FC7;&#xFF0C;&#x5BF9;&#x6B64;&#x56FE;&#x805A;&#x7C7B;&#x53EF;&#x4EE5;&#x53D1;&#x73B0;&#x7814;&#x7A76;&#x5174;&#x8DA3;&#x76F8;&#x8FD1;&#x7684;&#x5B66;&#x672F;&#x5C0F;&#x5708;&#x5B50;</p>
<p><br><br></p>
<p><span class="blue">&#x6574;&#x56FE;&#x5C42;&#x9762;&#x7684;&#x5206;&#x7C7B;&#x3001;&#x56DE;&#x5F52;&#x3001;&#x805A;&#x7C7B;</span></p>
<ul>
<li>&#x5BF9;&#x4E8E;&#x4E00;&#x6BB5;&#x8BA1;&#x7B97;&#x673A;&#x7A0B;&#x5E8F;&#xFF0C;&#x901A;&#x8FC7;&#x5BF9;&#x8BED;&#x6CD5;&#x6811;&#x8FDB;&#x884C;&#x5206;&#x7C7B;&#x5224;&#x65AD;&#x662F;&#x5426;&#x6709; bug</li>
<li>&#x901A;&#x8FC7;&#x5BF9;&#x5206;&#x5B50;&#x7ED3;&#x6784;&#x56DE;&#x5F52;&#xFF0C;&#x9884;&#x6D4B;&#x5206;&#x5B50;&#x7684;&#x6BD2;&#x6027;&#x3001;&#x6EB6;&#x89E3;&#x6027;&#x7B49;</li>
<li>&#x6700;&#x63A5;&#x8FD1;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4E2D;&#x5206;&#x7C7B;&#x548C;&#x56DE;&#x5F52;&#x7684;&#x8BBE;&#x5B9A;&#xFF0C;&#x6BCF;&#x5F20;&#x56FE;&#x53EF;&#x4EE5;&#x770B;&#x4F5C;&#x72EC;&#x7ACB;&#x540C;&#x5206;&#x5E03;&#x7684;&#x6709;&#x6807;&#x8BB0;&#x70B9;</li>
<li>&#x805A;&#x7C7B;&#x4E5F;&#x540C;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4E2D;&#x7684;&#x805A;&#x7C7B;&#xFF0C;&#x96BE;&#x70B9;&#x5728;&#x4E8E;&#x8BBE;&#x8BA1;&#x80FD;&#x8868;&#x5F81;&#x7ED3;&#x6784;&#x4FE1;&#x606F;&#x7684;&#x7279;&#x5F81;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="300" class="slide " data-line="300" data-h="3" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE;&#x7684;&#x7279;&#x5F81;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x4F20;&#x7EDF;&#x673A;&#x5668;&#x5B66;&#x4E60;&#xFF1A;</p>
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<!-- 原始(图)数据 -->
<g id="node1" class="node">
<title>&#x539F;&#x59CB;(&#x56FE;)&#x6570;&#x636E;</title>
<text text-anchor="middle" x="47.7736" y="-29.2" font-family="EBGaramond12-Regular,fz-lz" font-size="16.00" fill="#b58900">&#x539F;&#x59CB;(&#x56FE;)&#x6570;&#x636E;</text>
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<!-- 数据预处理 -->
<g id="node2" class="node">
<title>&#x6570;&#x636E;&#x9884;&#x5904;&#x7406;</title>
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<!-- 原始(图)数据&#45;&gt;数据预处理 -->
<g id="edge3" class="edge">
<title>&#x539F;&#x59CB;(&#x56FE;)&#x6570;&#x636E;-&gt;&#x6570;&#x636E;&#x9884;&#x5904;&#x7406;</title>
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<!-- 特征提取 -->
<g id="node3" class="node">
<title>&#x7279;&#x5F81;&#x63D0;&#x53D6;</title>
<text text-anchor="middle" x="270.2136" y="-29.2" font-family="EBGaramond12-Regular,fz-lz" font-size="16.00" fill="#b58900">&#x7279;&#x5F81;&#x63D0;&#x53D6;</text>
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<!-- 数据预处理&#45;&gt;特征提取 -->
<g id="edge1" class="edge">
<title>&#x6570;&#x636E;&#x9884;&#x5904;&#x7406;-&gt;&#x7279;&#x5F81;&#x63D0;&#x53D6;</title>
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<!-- 特征转换 -->
<g id="node4" class="node">
<title>&#x7279;&#x5F81;&#x8F6C;&#x6362;</title>
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<!-- 特征提取&#45;&gt;特征转换 -->
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<title>&#x7279;&#x5F81;&#x63D0;&#x53D6;-&gt;&#x7279;&#x5F81;&#x8F6C;&#x6362;</title>
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<!-- 预测 -->
<g id="node5" class="node">
<title>&#x9884;&#x6D4B;</title>
<text text-anchor="middle" x="470.968" y="-29.2" font-family="EBGaramond12-Regular,fz-lz" font-size="16.00" fill="#dc322f">&#x9884;&#x6D4B;</text>
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<!-- 特征转换&#45;&gt;预测 -->
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<!-- 结果 -->
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<title>&#x7ED3;&#x679C;</title>
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</g>
<!-- 预测&#45;&gt;结果 -->
<g id="edge5" class="edge">
<title>&#x9884;&#x6D4B;-&gt;&#x7ED3;&#x679C;</title>
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</p><br>
<p>&#x56FE;&#x7684;&#x54EA;&#x4E9B;<span class="blue">&#x7EDF;&#x8BA1;&#x91CF;</span>&#x53EF;&#x7528;&#x6765;&#x8BBE;&#x8BA1;&#x7279;&#x5F81;&#xFF1F;</p>
<ul>
<li>&#x70B9;&#x5C42;&#x9762;</li>
<li>&#x56FE;&#x5C42;&#x9762;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="358" class="slide " data-line="358" data-h="3" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x5BB6;&#x65CF;&#x901A;&#x5A5A;&#x56FE;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
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<g id="edge1" class="edge">
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<g id="edge3" class="edge">
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<g id="node10" class="node">
<title>Guadagni</title>
<text text-anchor="middle" x="306.2279" y="-132.0156" font-family="EBGaramond12-Regular,fz-lz" font-size="12.00" fill="#b58900">Guadagni</text>
</g>
<!-- Tornabuoni&#45;&gt;Guadagni -->
<g id="edge11" class="edge">
<title>Tornabuoni-&gt;Guadagni</title>
<path fill="none" stroke="#586e75" d="M269.9515,-144.4967C271.652,-144.0804 273.3525,-143.6641 275.038,-143.2514"/>
</g>
<!-- Ginori -->
<g id="node9" class="node">
<title>Ginori</title>
<text text-anchor="middle" x="222.7212" y="-14.4" font-family="EBGaramond12-Regular,fz-lz" font-size="12.00" fill="#b58900">Ginori</text>
</g>
<!-- Albizzi&#45;&gt;Ginori -->
<g id="edge8" class="edge">
<title>Albizzi-&gt;Ginori</title>
<path fill="none" stroke="#586e75" d="M223.1912,-80.0058C223.0917,-66.8797 222.958,-49.2375 222.8586,-36.1279"/>
</g>
<!-- Albizzi&#45;&gt;Guadagni -->
<g id="edge9" class="edge">
<title>Albizzi-&gt;Guadagni</title>
<path fill="none" stroke="#586e75" d="M249.1045,-109.8374C257.2795,-113.5266 266.4086,-117.6462 274.9281,-121.4908"/>
</g>
<!-- Strozzi -->
<g id="node11" class="node">
<title>Strozzi</title>
<text text-anchor="middle" x="277.1791" y="-258.9328" font-family="EBGaramond12-Regular,fz-lz" font-size="12.00" fill="#b58900">Strozzi</text>
</g>
<!-- Ridolfi&#45;&gt;Strozzi -->
<g id="edge12" class="edge">
<title>Ridolfi-&gt;Strozzi</title>
<path fill="none" stroke="#586e75" d="M240.1059,-232.7063C244.8534,-236.5259 249.863,-240.5562 254.6117,-244.3767"/>
</g>
<!-- Lamberteschi -->
<g id="node13" class="node">
<title>Lamberteschi</title>
<text text-anchor="middle" x="372.1379" y="-87.7513" font-family="EBGaramond12-Regular,fz-lz" font-size="12.00" fill="#b58900">Lamberteschi</text>
</g>
<!-- Guadagni&#45;&gt;Lamberteschi -->
<g id="edge14" class="edge">
<title>Guadagni-&gt;Lamberteschi</title>
<path fill="none" stroke="#586e75" d="M333.036,-117.6116C337.0277,-114.9308 341.1441,-112.1663 345.1396,-109.483"/>
</g>
<!-- Bischeri -->
<g id="node14" class="node">
<title>Bischeri</title>
<text text-anchor="middle" x="340.5605" y="-215.0922" font-family="EBGaramond12-Regular,fz-lz" font-size="12.00" fill="#b58900">Bischeri</text>
</g>
<!-- Guadagni&#45;&gt;Bischeri -->
<g id="edge15" class="edge">
<title>Guadagni-&gt;Bischeri</title>
<path fill="none" stroke="#586e75" d="M313.6776,-153.642C319.3969,-167.4813 327.2618,-186.5124 333.0068,-200.4141"/>
</g>
<!-- Strozzi&#45;&gt;Castellani -->
<g id="edge16" class="edge">
<title>Strozzi-&gt;Castellani</title>
<path fill="none" stroke="#586e75" d="M262.8569,-280.5729C258.0732,-286.5984 252.7404,-293.3156 247.943,-299.3583"/>
</g>
<!-- Strozzi&#45;&gt;Bischeri -->
<g id="edge17" class="edge">
<title>Strozzi-&gt;Bischeri</title>
<path fill="none" stroke="#586e75" d="M302.2291,-245.2058C306.243,-242.4295 310.4056,-239.5502 314.4436,-236.7572"/>
</g>
<!-- Peruzzi -->
<g id="node15" class="node">
<title>Peruzzi</title>
<text text-anchor="middle" x="319.9927" y="-297.3788" font-family="EBGaramond12-Regular,fz-lz" font-size="12.00" fill="#b58900">Peruzzi</text>
</g>
<!-- Strozzi&#45;&gt;Peruzzi -->
<g id="edge18" class="edge">
<title>Strozzi-&gt;Peruzzi</title>
<path fill="none" stroke="#586e75" d="M297.3322,-280.63C298.1998,-281.409 299.0701,-282.1906 299.9374,-282.9694"/>
</g>
<!-- Castellani&#45;&gt;Peruzzi -->
<g id="edge19" class="edge">
<title>Castellani-&gt;Peruzzi</title>
<path fill="none" stroke="#586e75" d="M265.6683,-311.4282C274.9926,-309.6346 285.0502,-307.7001 293.9466,-305.9888"/>
</g>
<!-- Bischeri&#45;&gt;Peruzzi -->
<g id="edge20" class="edge">
<title>Bischeri-&gt;Peruzzi</title>
<path fill="none" stroke="#586e75" d="M335.9959,-236.9543C332.5874,-250.5906 327.95,-269.1438 324.5446,-282.7678"/>
</g>
</g>
</svg>
</p><p style="width:32%;margin-left:65%;margin-top:-30%">
&#x54EA;&#x4E9B;&#x7EDF;&#x8BA1;&#x91CF;&#x80FD;&#x4F53;&#x73B0;&#x51FA;Medici&#x5BB6;&#x65CF;&#x7684;&#x5D1B;&#x8D77;&#xFF1F;
</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="414" class="slide " data-line="414" data-h="4" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x5EA6;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5EA6;(degree)&#xFF1A;&#x4E0E;&#x70B9;&#x76F8;&#x8FDE;&#x7684;&#x8FB9;&#x7684;&#x6570;&#x76EE;</p>
<div>
    $$
        \begin{align*}
            d_u = \sum_{v \in \Vcal} [\Av]_{uv}
        \end{align*}
    $$
</div>
<br>
<p>&#x5EA6;&#x4E0E;&#x8FB9;&#x7684;&#x5173;&#x7CFB;</p>
<div>
    $$
        \begin{align*}
            \sum_{u \in \Vcal} d_u = 2 |\Ecal|
        \end{align*}
    $$
</div>
<br>
<p>&#x5BF9;&#x4E8E;&#x5BB6;&#x65CF;&#x901A;&#x5A5A;&#x56FE;</p>
<ul>
<li>Medici &#x7684;&#x5EA6;&#x6570;&#x662F;<span class="mathjax-exps">$5$</span>&#xFF0C;&#x6700;&#x5927;&#x7684;&#x5BB6;&#x65CF;</li>
<li>Guadagn &#x548C; Strozzi &#x7684;&#x5EA6;&#x6570;&#x662F;<span class="mathjax-exps">$4$</span></li>
<li>&#x533A;&#x5206;&#x5EA6;&#x4E0D;&#x592A;&#x660E;&#x663E;&#xFF0C;&#x9700;&#x8981;&#x66F4;&#x5F3A;&#x7684;&#x7279;&#x5F81;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="462" class="slide " data-line="462" data-h="4" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x4E2D;&#x5FC3;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x8BB0;&#x90BB;&#x63A5;&#x77E9;&#x9635;<span class="mathjax-exps">$\Av$</span>&#x7684;&#x6700;&#x5927;&#x7279;&#x5F81;&#x503C;/&#x5411;&#x91CF;&#x4E3A;<span class="mathjax-exps">$(\lambda_1, \vv_1)$</span>&#xFF0C;&#x5219;&#x70B9;<span class="mathjax-exps">$u$</span>&#x7684;<span class="blue">&#x7279;&#x5F81;&#x5411;&#x91CF;&#x4E2D;&#x5FC3;</span>&#x4E3A;<span class="mathjax-exps">$[\vv_1]_u$</span></p>
<div>
    $$
        \begin{align*}
            \lambda_1 \vv_1 = \Av \vv_1 \Longrightarrow [\vv_1]_u = \frac{1}{\lambda_1} \sum_{v \in \Vcal} [\Av]_{uv} [\vv_1]_v
        \end{align*}
    $$
</div>
<p>&#x6BCF;&#x4E2A;&#x70B9;&#x7684;&#x7279;&#x5F81;&#x5411;&#x91CF;&#x4E2D;&#x5FC3;&#x7531;&#x5176;&#x90BB;&#x5C45;&#x51B3;&#x5B9A;&#xFF1A;&#x4F60;&#x670B;&#x53CB;&#x90FD;&#x662F;&#x5927;&#x725B;&#x90A3;&#x4F60;&#x80AF;&#x5B9A;&#x4E5F;&#x725B;</p>
<br>
<p>&#x53E6;&#x4E00;&#x4E2A;&#x89C6;&#x89D2;&#xFF1A;&#x7531;<span class="blue">Power Method</span>(&#x53C2;&#x89C1;&#x4E0B;&#x4E00;&#x9875;)&#x77E5;</p>
<div>
    $$
        \begin{align*}
            \lim_{t \rightarrow \infty} \Av^t \ev \class{yellow}{\propto \vv_1}
        \end{align*}
    $$
</div>
<p>&#x53C8;<span class="mathjax-exps">$[\Av^t]_{uv}$</span>&#x8868;&#x793A;&#x70B9;<span class="mathjax-exps">$u$</span>&#x5230;&#x70B9;<span class="mathjax-exps">$v$</span>&#x7684;&#x957F;&#x5EA6;&#x4E3A;<span class="mathjax-exps">$t$</span>&#x7684;&#x8DEF;&#x5F84;&#x6570;&#xFF0C;&#x6545;&#x7279;&#x5F81;&#x5411;&#x91CF;&#x4E2D;&#x5FC3;&#x6B63;&#x6BD4;&#x4E8E;<span class="blue">&#x53EF;&#x88AB;&#x5176;&#x4ED6;&#x70B9;&#x901A;&#x8FC7;&#x65E0;&#x9650;&#x957F;&#x7684;&#x8DEF;&#x5F84;&#x8BBF;&#x95EE;&#x7684;&#x603B;&#x6B21;&#x6570;</span></p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="506" class="slide " data-line="506" data-h="5" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">Power Method</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x8BBE;<span class="mathjax-exps">$\Av$</span>&#x4E3A;&#x5B9E;&#x5BF9;&#x79F0;&#x77E9;&#x9635;&#xFF0C;&#x5373;<span class="mathjax-exps">$\Av$</span>&#x53EF;&#x5BF9;&#x89D2;&#x5316;&#x4E14;&#x7279;&#x5F81;&#x503C;<span class="mathjax-exps">$\lambda_1, \ldots, \lambda_n$</span>&#x5747;&#x4E3A;&#x5B9E;&#x6570;&#xFF0C;&#x8BBE;<span class="mathjax-exps">$\lambda_1$</span>&#x662F;&#x7EDD;&#x5BF9;&#x503C;&#x6700;&#x5927;&#x7684;&#x7279;&#x5F81;&#x503C;&#x4E14;&#x91CD;&#x6570;&#x4E3A;<span class="mathjax-exps">$1$</span>&#xFF0C;&#x5373;<span class="mathjax-exps">$|\lambda_1| &gt; \{ |\lambda_i| \}_{i \neq 1}$</span>&#xFF0C;<span class="mathjax-exps">$\lambda_1$</span>&#x5BF9;&#x5E94;&#x7684;&#x7279;&#x5F81;&#x5411;&#x91CF;&#x4E3A;<span class="mathjax-exps">$\vv_1$</span>&#xFF0C;&#x521D;&#x59CB;&#x53D6;<span class="mathjax-exps">$\xv_0$</span>&#x4E3A;&#x4EFB;&#x610F;&#x5411;&#x91CF;&#xFF0C;&#x5E76;&#x4F9D;</p>
<div>
    $$
        \begin{align*}
            \xv_k = \frac{\Av \xv_{k-1}}{\|\Av \xv_{k-1}\|}
        \end{align*}
    $$
</div>
<p>&#x8FED;&#x4EE3;&#xFF0C;&#x5219;&#x6709;<span class="mathjax-exps">$\lim_{k \rightarrow \infty} \xv_k = \vv_1$</span></p>
<br>
<p>&#x8BC1;&#x660E;&#xFF1A;&#x6613;&#x77E5;</p>
<div>
    $$
    \begin{align*}
        \xv_k = \frac{\Av \xv_{k-1}}{\|\Av \xv_{k-1}\|} = \frac{\Av \frac{\Av \xv_{k-2}}{\|\Av \xv_{k-2}\|}}{\|\Av \frac{\Av \xv_{k-2}}{\|\Av \xv_{k-2}\|}\|} = \frac{\Av^2 \xv_{k-2}}{\|\Av^2 \xv_{k-2}\|} = \cdots = \frac{\Av^k \xv_0}{\|\Av^k \xv_0\|}
    \end{align*}
    $$
</div>
<p>&#x8BBE;<span class="mathjax-exps">$\xv_0 = c_1 \vv_1 + \cdots + c_n \vv_n$</span>&#xFF0C;&#x5219;</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="550" class="slide " data-line="550" data-h="5" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">Power Method</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<div>
    $$
    \begin{align*}
        \Av^k \xv_0 &amp; = \Av^{k-1} \Av (c_1 \vv_1 + \cdots + c_n \vv_n) = \Av^{k-1} (c_1 \lambda_1 \vv_1 + \cdots + c_n \lambda_n \vv_n) \\
        &amp; = \Av^{k-2} (c_1 \lambda_1^2 \vv_1 + \cdots + c_n \lambda_n^2 \vv_n) = c_1 \lambda_1^k \vv_1 + \cdots + c_n \lambda_n^k \vv_n
    \end{align*}
    $$
</div>
<p>&#x4ECE;&#x800C;</p>
<div>
    $$
        \begin{align*}
            \xv_k &amp; = \frac{\Av^k \xv_0}{\|\Av^k \xv_0\|} = \frac{c_1 \lambda_1^k \vv_1 + \cdots + c_n \lambda_n^k \vv_n}{\|c_1 \lambda_1^k \vv_1 + \cdots + c_n \lambda_n^k \vv_n\|} \\
            &amp; = \frac{c_1}{|c_1|} \left( \frac{\lambda_1}{|\lambda_1|} \right)^k \frac{\vv_1 + \frac{c_2}{c_1} (\frac{\lambda_2}{\lambda_1})^k \vv_2 + \cdots + \frac{c_n}{c_1} (\frac{\lambda_n}{\lambda_1})^k \vv_n}{\| \vv_1 + \frac{c_2}{c_1} (\frac{\lambda_2}{\lambda_1})^k \vv_2 + \cdots + \frac{c_n}{c_1} (\frac{\lambda_n}{\lambda_1})^k \vv_n \|} \\
            &amp; = \sign(c_1)~(\sign(\lambda_1))^k~\frac{\vv_1 + \frac{c_2}{c_1} (\frac{\lambda_2}{\lambda_1})^k \vv_2 + \cdots + \frac{c_n}{c_1} (\frac{\lambda_n}{\lambda_1})^k \vv_n}{\| \vv_1 + \frac{c_2}{c_1} (\frac{\lambda_2}{\lambda_1})^k \vv_2 + \cdots + \frac{c_n}{c_1} (\frac{\lambda_n}{\lambda_1})^k \vv_n \|} \\
            &amp; \rightarrow \sign(c_1)~(\sign(\lambda_1))^k \vv_1, \qquad \lim_{k \rightarrow \infty} \left( \frac{\lambda_i}{\lambda_1} \right)^k = 0
        \end{align*}
    $$
</div>
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        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="590" class="slide " data-line="590" data-h="5" data-v="2">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">Power Method</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5DF2;&#x8BC1; <span class="mathjax-exps">$\xv_k \rightarrow \sign(c_1)~(\sign(\lambda_1))^k \vv_1$</span>&#xFF0C;&#x5206;&#x4E24;&#x79CD;&#x60C5;&#x51B5;&#xFF1A;</p>
<ol>
<li><span class="mathjax-exps">$\lambda_1 &gt; 0$</span>&#xFF0C;&#x5219;<span class="mathjax-exps">$\sign(\lambda_1) = 1$</span>&#xFF0C;<span class="mathjax-exps">$\xv_{k-1} \approx \sign(c_1) \vv_1$</span>&#xFF0C;<span class="mathjax-exps">$\xv_k \approx \sign(c_1) \vv_1$</span>&#xFF0C;&#x4E8E;&#x662F;</li>
</ol>
<div>
    $$
        \begin{align*}
            \sign(c_1) \vv_1 \approx \xv_k &amp; = \frac{\Av \xv_{k-1}}{\|\Av \xv_{k-1}\|} \approx \frac{\Av \sign(c_1) \vv_1}{\|\Av \xv_{k-1}\|} = \frac{\sign(c_1) \lambda_1 \vv_1}{\|\Av \xv_{k-1}\|} \\
            &amp; \Rightarrow \lambda_1 \approx \|\Av \xv_{k-1}\|
        \end{align*}
    $$
</div>
<ol start="2">
<li><span class="mathjax-exps">$\lambda_1 &lt; 0$</span>&#xFF0C;<span class="mathjax-exps">$\xv_k$</span>&#x4EA4;&#x66FF;&#x8D8B;&#x5411;<span class="mathjax-exps">$\pm \sign(c_1) \vv_1$</span>&#xFF0C;&#x4E0D;&#x59A8;&#x8BBE;<span class="mathjax-exps">$\xv_{k-1} \approx \sign(c_1) \vv_1$</span>&#xFF0C;<span class="mathjax-exps">$\xv_k \approx -\sign(c_1) \vv_1$</span></li>
</ol>
<div>
    $$
        \begin{align*}
            -\sign(c_1) \vv_1 \approx \xv_k &amp; = \frac{\Av \xv_{k-1}}{\|\Av \xv_{k-1}\|} \approx \frac{\Av \sign(c_1) \vv_1}{\|\Av \xv_{k-1}\|} = \frac{\sign(c_1) \lambda_1 \vv_1}{\|\Av \xv_{k-1}\|} \\
            &amp; \Rightarrow \lambda_1 \approx -\|\Av \xv_{k-1}\|
        \end{align*}
    $$
</div>
<ul>
<li>Power Method &#x7684;&#x6761;&#x4EF6;&#x4E2D;<span class="mathjax-exps">$\Av$</span>&#x5BF9;&#x79F0;&#x4E0D;&#x662F;&#x5FC5;&#x9700;&#x7684;&#xFF0C;&#x867D;&#x7136;&#x975E;&#x5BF9;&#x79F0;&#x77E9;&#x9635;&#x4E0D;&#x4E00;&#x5B9A;&#x80FD;&#x5BF9;&#x89D2;&#x5316;&#xFF0C;&#x4F46;&#x901A;&#x8FC7;&#x8F6C;&#x6362;&#x6210; Jordan &#x6807;&#x51C6;&#x578B;&#x7684;&#x5F62;&#x5F0F;&#x4F9D;&#x7136;&#x53EF;&#x4EE5;&#x8BC1;&#x660E;&#x524D;&#x9762;&#x7684;&#x7ED3;&#x8BBA;</li>
<li>&#x5BF9;&#x4E8E;&#x6709;&#x5411;&#x56FE;&#xFF0C;&#x90BB;&#x63A5;&#x77E9;&#x9635;<span class="mathjax-exps">$\Av$</span>&#x975E;&#x5BF9;&#x79F0;&#xFF0C;&#x4F46;&#x4F9D;&#x7136;&#x53EF;&#x4EE5;&#x4F7F;&#x7528; Power Method</li>
</ul>
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        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="635" class="slide " data-line="635" data-h="6" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x4E2D;&#x5FC3;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5BF9;&#x4E8E;&#x5BB6;&#x65CF;&#x901A;&#x5A5A;&#x56FE;&#xFF0C;Medici &#x7684;&#x7279;&#x5F81;&#x5411;&#x91CF;&#x4E2D;&#x5FC3;&#x503C;&#x4E3A;<span class="mathjax-exps">$0.43$</span>&#xFF0C;&#x7B2C;&#x4E8C;&#x5927;&#x7684;&#x4E3A;<span class="mathjax-exps">$0.36$</span></p>
<br>
<p>&#x9664;&#x4E86;&#x7279;&#x5F81;&#x5411;&#x91CF;&#x4E2D;&#x5FC3;&#x5916;&#x8FD8;&#x6709;</p>
<ul>
<li><span class="blue">&#x4ECB;</span>(betweeness)&#x4E2D;&#x5FC3;&#xFF1A;&#x4E00;&#x4E2A;&#x70B9;&#x5728;&#x5176;&#x5B83;&#x4E24;&#x4E2A;&#x6700;&#x77ED;&#x8DEF;&#x5F84;&#x4E0A;&#x7684;&#x9891;&#x7387;</li>
<li><span class="blue">&#x95ED;</span>(closeness)&#x4E2D;&#x5FC3;&#xFF1A;&#x4E00;&#x4E2A;&#x70B9;&#x5230;&#x5176;&#x5B83;&#x70B9;&#x7684;&#x5E73;&#x5747;&#x6700;&#x77ED;&#x8DEF;&#x5F84;</li>
</ul>
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    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="662" class="slide " data-line="662" data-h="6" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x805A;&#x7C7B;&#x7CFB;&#x6570;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5EA6;&#x548C;&#x4E2D;&#x5FC3;&#x80FD;&#x533A;&#x5206;&#x51FA;&#x6700;&#x5F3A;&#x7684; Medici &#x5BB6;&#x65CF;&#xFF0C;&#x4F46;&#x5BF9;&#x4E8E; Peruzzi &#x5BB6;&#x65CF;&#x548C; Guadagn &#x5BB6;&#x65CF;&#x533A;&#x5206;&#x5EA6;&#x4E0D;&#x5F3A;&#xFF1A;</p>
<ul>
<li>&#x5EA6;&#x5206;&#x522B;&#x662F;<span class="mathjax-exps">$3$</span>&#x3001;<span class="mathjax-exps">$4$</span></li>
<li>&#x7279;&#x5F81;&#x5411;&#x91CF;&#x4E2D;&#x5FC3;&#x5206;&#x522B;&#x662F;<span class="mathjax-exps">$0.28$</span>&#x3001;<span class="mathjax-exps">$0.29$</span></li>
</ul>
<br>
<p>&#x805A;&#x7C7B;&#x7CFB;&#x6570;(clustering coefficient)&#xFF1A;&#x90BB;&#x5C45;&#x95F4;&#x7684;&#x7D27;&#x5BC6;&#x7A0B;&#x5EA6;</p>
<div>
    $$
        \begin{align*}
            c_u = \frac{|(v_1, v_2) \in \Ecal : v_1, v_2 \in \Ncal(u)|}{d_u (d_u - 1) / 2}
        \end{align*}
    $$
</div>
<p>&#x5206;&#x5B50;&#x662F;<span class="mathjax-exps">$u$</span>&#x7684;&#x6240;&#x6709;&#x90BB;&#x5C45;&#x95F4;&#x7684;&#x8FB9;&#x6570;&#xFF0C;&#x805A;&#x7C7B;&#x7CFB;&#x6570;&#x4E3A;<span class="mathjax-exps">$1$</span>&#x4EE3;&#x8868;&#x6240;&#x6709;&#x90BB;&#x5C45;&#x90FD;&#x4E92;&#x4E3A;&#x90BB;&#x5C45;</p>
<br>
<p>&#x5BF9;&#x4E8E;&#x5BB6;&#x65CF;&#x901A;&#x5A5A;&#x56FE;</p>
<ul>
<li>Peruzzi &#x7684;&#x805A;&#x7C7B;&#x7CFB;&#x6570;&#x662F;<span class="mathjax-exps">$0.66$</span></li>
<li>Guadagn &#x7684;&#x805A;&#x7C7B;&#x7CFB;&#x6570;&#x662F;<span class="mathjax-exps">$0$</span></li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="706" class="slide " data-line="706" data-h="6" data-v="2">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x81EA;&#x6211;&#x56FE;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x81EA;&#x6211;&#x56FE;(ego graph)&#x662F;&#x4E00;&#x4E2A;&#x70B9;&#x7684;&#x90BB;&#x57DF;&#x5B50;&#x56FE;</p>
<ul>
<li>&#x5305;&#x542B;&#x8BE5;&#x70B9;&#x53CA;&#x5176;&#x6240;&#x6709;&#x90BB;&#x5C45;</li>
<li>&#x5305;&#x542B;&#x4E0A;&#x8FF0;&#x6240;&#x6709;&#x70B9;&#x7684;&#x5185;&#x90E8;&#x8FDE;&#x8FB9;</li>
</ul>
<br>
<p>&#x805A;&#x7C7B;&#x7CFB;&#x6570; = &#x81EA;&#x6211;&#x56FE;&#x4E2D;&#x7684;&#x4E09;&#x89D2;&#x5F62;&#x7684;&#x4E2A;&#x6570; / &#x4E09;&#x89D2;&#x5F62;&#x7684;&#x6700;&#x5927;&#x53EF;&#x80FD;&#x6570;</p>
<br>
<p>&#x63A8;&#x5E7F;&#xFF1A;&#x8003;&#x8651;&#x66F4;&#x590D;&#x6742;&#x7684;&#x56FE;&#x5F62;&#x7ED3;&#x6784;&#xFF0C;&#x6BD4;&#x5982;&#x56DB;&#x8FB9;&#x5F62;</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="737" class="slide " data-line="737" data-h="7" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE;&#x7684;&#x7EDF;&#x8BA1;&#x91CF;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x70B9;&#x5C42;&#x9762;&#x7684;&#x7EDF;&#x8BA1;&#x91CF;&#x53EF;&#x5E94;&#x7528;&#x4E8E;&#x70B9;&#x5C42;&#x9762;&#x7684;&#x4EFB;&#x52A1;</p>
<ul>
<li>&#x5EA6;</li>
<li>&#x4E2D;&#x5FC3;</li>
<li>&#x805A;&#x7C7B;&#x7CFB;&#x6570;</li>
<li>&#x81EA;&#x6211;&#x56FE;&#x5BFC;&#x51FA;&#x7684;&#x5E7F;&#x4E49;&#x805A;&#x7C7B;&#x7CFB;&#x6570;</li>
</ul>
<br>
<p>&#x7C7B;&#x4F3C;&#x7684;&#xFF0C;&#x56FE;&#x5C42;&#x9762;&#x7684;&#x7EDF;&#x8BA1;&#x91CF;&#x53EF;&#x5E94;&#x7528;&#x4E8E;&#x56FE;&#x5C42;&#x9762;&#x7684;&#x4EFB;&#x52A1;</p>
<ul>
<li>&#x9690;&#x5F0F;&#xFF1A;&#x56FE;&#x6838;(graph kernel)</li>
<li>&#x663E;&#x5F0F;&#xFF1A;&#x6C47;&#x96C6;&#x70B9;&#x5C42;&#x9762;&#x7684;&#x7EDF;&#x8BA1;&#x91CF;&#xFF0C;&#x8BA1;&#x7B97;&#x5B50;&#x7ED3;&#x6784;&#x51FA;&#x73B0;&#x7684;&#x6B21;&#x6570;</li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="769" class="slide " data-line="769" data-h="7" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x56FE;&#x6838;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x7ED9;&#x5B9A;&#x4E24;&#x4E2A;&#x56FE;<span class="mathjax-exps">$\Gcal_1 = (\Vcal_1, \Ecal_1)$</span>&#x548C;<span class="mathjax-exps">$\Gcal_2 = (\Vcal_2, \Ecal_2)$</span>&#x548C;&#x56FE;&#x5206;&#x89E3;&#x65B9;&#x5F0F;<span class="mathjax-exps">$\Fcal$</span></p>
<div>
    $$
        \begin{align*}
            &amp; \Fcal (\Gcal_1) = \{ \Scal_{1,1}, \ldots, \Scal_{1,m_1} \}, \quad \Fcal (\Gcal_2) = \{ \Scal_{2,1}, \ldots, \Scal_{2,m_2} \} \\
            &amp; \kappa (\Gcal_1, \Gcal_2) = \sum_{i \in [m_1]} \sum_{j \in [m_2]} \delta (\Scal_{1,i}, \Scal_{2,j})
        \end{align*}
    $$
</div>
<p>&#x5176;&#x4E2D;<span class="mathjax-exps">$\delta (\cdot, \cdot)$</span>&#x53EF;&#x4EE5;&#x4E3A;&#x5728;&#x4E24;&#x4E2A;&#x8F93;&#x5165;&#x540C;&#x6784;&#x65F6;&#x4E3A;<span class="mathjax-exps">$1$</span>&#xFF0C;&#x4E0D;&#x540C;&#x6784;&#x65F6;&#x4E3A;<span class="mathjax-exps">$0$</span></p>
<br>
<div>
    $$
        \begin{align*}
            \mbox{SVM:} \quad \min_{\alpha_i,\alpha_j} &amp; ~ \frac{1}{2} \sum_{i,j \in [m]} \alpha_i \alpha_j y_i y_j \class{yellow}{\kappa(\xv_i, \xv_j)} - \sum_{i \in [m]} \alpha_i \quad \st ~ 0 \leq \alpha_i \leq C \\
            &amp; \qquad \qquad \qquad \qquad \Downarrow \\
            \min_{\alpha_i,\alpha_j} &amp; ~ \frac{1}{2} \sum_{i,j \in [m]} \alpha_i \alpha_j y_i y_j \class{yellow}{\kappa (\Gcal_1, \Gcal_2)} - \sum_{i \in [m]} \alpha_i \quad \st ~ 0 \leq \alpha_i \leq C
        \end{align*}
    $$
</div>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="812" class="slide " data-line="812" data-h="7" data-v="2">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x6C47;&#x96C6;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x6C47;&#x96C6;&#x70B9;&#x5C42;&#x9762;&#x7684;&#x7EDF;&#x8BA1;&#x91CF;&#x53EF;&#x80FD;&#x4E22;&#x5931;&#x56FE;&#x7684;&#x5168;&#x5C40;&#x4FE1;&#x606F;</p>
<br>
<p>&#x6539;&#x8FDB;&#x65B9;&#x6848;&#xFF1A;Weisfeiler-Lehman &#x7B97;&#x6CD5;</p>
<ol>
<li>&#x8D4B;&#x4E88;&#x6240;&#x6709;&#x70B9;&#x521D;&#x59CB;&#x6807;&#x8BB0;<span class="mathjax-exps">$l^{(0)} (v) = d_v$</span></li>
<li>&#x901A;&#x8FC7;&#x54C8;&#x5E0C;&#x51FD;&#x6570;&#x4E0D;&#x65AD;&#x66F4;&#x65B0;&#x6807;&#x8BB0;<span class="mathjax-exps">$l^{(i)} (v) = h(\{ l^{(i-1)} (u), ~ \forall u \in \Ncal(v)  \})$</span></li>
<li>&#x91CD;&#x590D;&#x4E0A;&#x4E00;&#x6B65;<span class="mathjax-exps">$K$</span>&#x6B21;&#x540E;&#x5F97;&#x5230;<span class="mathjax-exps">$l^{(K)} (v)$</span>&#xFF0C;&#x8BE5;&#x503C;&#x7F16;&#x7801;&#x4E86;&#x6BCF;&#x4E2A;&#x70B9;&#x7684;<span class="mathjax-exps">$K$</span>&#x9636;&#x90BB;&#x5C45;&#x7684;&#x7ED3;&#x6784;&#x4FE1;&#x606F;</li>
<li>&#x6839;&#x636E;&#x6240;&#x6709;&#x7684;<span class="mathjax-exps">$l^{(K)} (v)$</span>&#x8BA1;&#x7B97;&#x56FE;&#x7684;&#x5168;&#x5C40;&#x7EDF;&#x8BA1;&#x91CF;</li>
</ol>
<br>
<p>Weisfeiler-Lehman &#x7B97;&#x6CD5;&#x6709;&#x5F88;&#x6DF1;&#x7684;&#x7406;&#x8BBA;&#x80CC;&#x666F;&#xFF0C;&#x53EF;&#x4EE5;&#x89E3;&#x51B3;&#x4E00;&#x5927;&#x7C7B;&#x7684;&#x56FE;&#x540C;&#x6784;&#x95EE;&#x9898;</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="845" class="slide " data-line="845" data-h="7" data-v="3">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x5B50;&#x7ED3;&#x6784;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x7EDF;&#x8BA1;&#x5B50;&#x7ED3;&#x6784;&#x51FA;&#x73B0;&#x7684;&#x6B21;&#x6570;&#xFF0C;&#x5E38;&#x89C1;&#x7684;&#x5B50;&#x7ED3;&#x6784;&#xFF1A;</p>
<ul>
<li>&#x8DEF;&#x5F84;(path)</li>
<li>&#x5C0F;&#x56FE;(graphlet)</li>
</ul>
<br>
<p>&#x5BF9;&#x4E8E;&#x8DEF;&#x5F84;&#xFF0C;&#x53EF;&#x4EE5;&#x8003;&#x8651;&#x4EFB;&#x4E24;&#x70B9;&#x95F4;&#x7684;</p>
<ul>
<li>&#x4E0D;&#x540C;&#x957F;&#x5EA6;&#x7684;&#x8DEF;&#x5F84;&#x6570;</li>
<li>&#x6700;&#x77ED;&#x957F;&#x5EA6;&#x8DEF;&#x5F84;</li>
</ul>
<br>
<p>&#x901A;&#x8FC7;&#x8DEF;&#x5F84;&#x6216;&#x8005;&#x968F;&#x673A;&#x6E38;&#x8D70;&#x6765;&#x8BA1;&#x7B97;&#x56FE;&#x7684;&#x5168;&#x5C40;&#x4FE1;&#x606F;&#xFF0C;&#x53EF;&#x4EE5;&#x907F;&#x514D;&#x7EC4;&#x5408;&#x7206;&#x70B8;&#x7684;&#x95EE;&#x9898;</p>
<div class="footer">
    <hr class="hr_bottom">
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        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="879" class="slide " data-line="879" data-h="7" data-v="4">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x5C0F;&#x56FE;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<img src="data:image/svg+xml;charset=utf-8;base64,<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<div>
    $$
        \begin{align*}
            [\Sv]_{uv} &amp; = |\Ncal(u) \cap \Ncal(v)|
        \end{align*}
    $$
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<div>
    $$
        \begin{align*}
            [\Sv_{\text{Sorenson}}]_{uv} &amp; = \frac{2|\Ncal(u) \cap \Ncal(v)|}{d_u + d_v} \\
            [\Sv_{\text{Salton}}]_{uv} &amp; = \frac{2|\Ncal(u) \cap \Ncal(v)|}{\sqrt{d_u d_v}} \\
            [\Sv_{\text{Jaccard}}]_{uv} &amp; = \frac{|\Ncal(u) \cap \Ncal(v)|}{|\Ncal(u) \cup \Ncal(v)|}
        \end{align*}
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<p>&#x5C06;&#x5171;&#x540C;&#x90BB;&#x5C45;&#x7684;&#x91CD;&#x8981;&#x6027;&#x4E5F;&#x8003;&#x8651;&#x8FDB;&#x6765;</p>
<br>
<p>&#x5EA6;&#x6570;&#x8D8A;&#x4F4E;&#x7684;&#x5171;&#x540C;&#x90BB;&#x5C45;&#x8D8A;&#x6709;&#x4EF7;&#x503C;</p>
<br>
<p>&#x8D44;&#x6E90;&#x5B9A;&#x4F4D;(Resource Allocation)&#x6307;&#x6570;</p>
<div>
    $$
        \begin{align*}
            [\Sv_{\text{RA}}]_{uv} &amp; = \sum_{u \in \Ncal(v_1) \cap \Ncal(v_2)} \frac{1}{d_u}
        \end{align*}
    $$
</div>
<br>
<p>AA(Adamic-Adar)&#x6307;&#x6570;</p>
<div>
    $$
        \begin{align*}
            [\Sv_{\text{AA}}]_{uv} &amp; = \sum_{u \in \Ncal(v_1) \cap \Ncal(v_2)} \frac{1}{\log(d_u)}
        \end{align*}
    $$
</div>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="993" class="slide " data-line="993" data-h="9" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x5168;&#x5C40;&#x91CD;&#x5408;&#x5EA6;&#x91CF;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5BF9;&#x4E8E;&#x94FE;&#x63A5;&#x9884;&#x6D4B;&#x4EFB;&#x52A1;&#x6765;&#x8BF4;</p>
<ul>
<li>&#x5C40;&#x90E8;&#x91CD;&#x5408;&#x5EA6;&#x91CF;&#x5C31;&#x5DF2;&#x7ECF;&#x5F88;&#x5F3A;&#x4E86;&#xFF0C;&#x5F80;&#x5F80;&#x4E0D;&#x900A;&#x4E8E;&#x7CBE;&#x5FC3;&#x8BBE;&#x8BA1;&#x7684;&#x6DF1;&#x5EA6;&#x5B66;&#x4E60;&#x7B97;&#x6CD5;</li>
<li>&#x4F46;&#x4E00;&#x65E6;&#x4E24;&#x4E2A;&#x70B9;&#x6CA1;&#x6709;&#x5171;&#x540C;&#x90BB;&#x5C45;&#x5C31;&#x6B47;&#x83DC;&#x4E86;&#xFF0C;&#x80AF;&#x5B9A;&#x9884;&#x6D4B;&#x4E0D;&#x51FA;&#x6765;</li>
</ul>
<br>
<p>&#x6539;&#x8FDB;&#x65B9;&#x6848;&#xFF1A;&#x8003;&#x8651;&#x4E24;&#x4E2A;&#x70B9;&#x4E4B;&#x95F4;&#x7684;&#x8DEF;&#x5F84;</p>
<br>
<p>Katz &#x6307;&#x6570;</p>
<div>
    $$
        \begin{align*}
            [\Sv_{\text{Katz}}]_{uv} &amp; = \sum_{i=1}^\infty \beta^i [\Av^i]_{uv}
        \end{align*}
    $$
</div>
<p>&#x5176;&#x4E2D;&#x53C2;&#x6570;<span class="mathjax-exps">$\beta &lt; 1$</span>&#x7528;&#x6765;&#x9002;&#x5F53;&#x964D;&#x4F4E;&#x957F;&#x8DEF;&#x5F84;&#x7684;&#x6743;&#x91CD;</p>
<br>
<p>&#x95EE;&#x9898;&#xFF1A;&#x5982;&#x4F55;&#x8BA1;&#x7B97;&#xFF1F;</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="1038" class="slide " data-line="1038" data-h="9" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">Katz&#x6307;&#x6570;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5F53;<span class="mathjax-exps">$|q| &lt; 1$</span>&#x65F6;</p>
<div>
    $$
        \begin{align*}
            \frac{1}{1-q} = 1 + q + q^2 + \cdots = \sum_{i=0}^\infty q^i
        \end{align*}
    $$
</div>
<p>&#x7C7B;&#x4F3C;&#x7684;&#xFF0C;&#x82E5;<span class="mathjax-exps">$\lambda_1 (\Av) &lt; 1$</span>&#xFF0C;&#x5219;</p>
<div>
    $$
        \begin{align*}
            (\Iv - \Av)^{-1} = \Iv + \Av + \Av^2 + \cdots = \sum_{i=0}^\infty \Av^i
        \end{align*}
    $$
</div>
<p>&#x4E8E;&#x662F;</p>
<div>
    $$
        \begin{align*}
            \Sv_{\text{Katz}} = \sum_{i=1}^\infty \beta^i \Av^i = \sum_{i=0}^\infty (\beta \Av)^i - \Iv = (\Iv - \beta \Av)^{-1} - \Iv
        \end{align*}
    $$
</div>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="1086" class="slide " data-line="1086" data-h="9" data-v="2">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">LNH&#x6307;&#x6570;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>Katz &#x6307;&#x6570;&#x4F1A;&#x504F;&#x5411;&#x4E8E;&#x5EA6;&#x6570;&#x8F83;&#x9AD8;&#x7684;&#x70B9;</p>
<p>&#x5F52;&#x4E00;&#x5316;&#xFF1A;<span class="mathjax-exps">$\Av^i / \Ebb [\Av^i]$</span>&#xFF0C;&#x5176;&#x4E2D;<span class="mathjax-exps">$\Ebb [\cdot]$</span>&#x5BF9;&#x62E5;&#x6709;&#x76F8;&#x540C;&#x70B9;&#x3001;&#x76F8;&#x540C;&#x5EA6;&#x6570;&#x7684;&#x968F;&#x673A;&#x56FE;&#x6C42;&#x671F;&#x671B;</p>
<p>&#x4ECE;&#x70B9;<span class="mathjax-exps">$u$</span>&#x51FA;&#x53D1;&#x7684;&#x8FB9;&#xFF0C;&#x4EE5;<span class="mathjax-exps">$d_v / \sum_i d_i$</span>&#x7684;&#x6982;&#x7387;&#x8FDE;&#x63A5;&#x70B9;<span class="mathjax-exps">$v$</span></p>
<div>
    $$
        \begin{align*}
            \Ebb [[\Av]_{uv}] &amp; = d_u \frac{d_v}{\sum_i d_i} = \frac{d_u d_v}{2 |\Ecal|} \\
            \Ebb [[\Av]_{uv}^2] &amp; = \sum_{w \in \Vcal} \frac{d_u d_w}{2 |\Ecal|} \frac{(d_w - 1) d_v}{2 |\Ecal|} = \frac{d_u d_v}{(2 |\Ecal|)^2} \sum_{w \in \Vcal} d_w (d_w - 1)
        \end{align*}
    $$
</div>
<p>&#x4F46;<span class="mathjax-exps">$i &gt; 2$</span>&#x65F6;&#x5C31;&#x4E0D;&#x80FD;&#x5982;&#x6CD5;&#x70AE;&#x5236;&#x4E86;&#xFF0C;&#x501F;&#x7531; Power Method &#x7684;&#x7ED3;&#x8BBA;&#x5BF9;&#x5145;&#x5206;&#x5927;&#x7684;<span class="mathjax-exps">$i$</span>&#x6709;</p>
<div>
    $$
        \begin{align*}
            \lambda_1 \pv_i = \Av \pv_i = \Av \Av^i \ev = \pv_{i+1}
        \end{align*}
    $$
</div>
<p>&#x5176;&#x4E2D;<span class="mathjax-exps">$p_i = \Av^i \ev$</span>&#x8868;&#x793A;&#x6BCF;&#x4E2A;&#x70B9;&#x53EF;&#x88AB;&#x5176;&#x4ED6;&#x70B9;&#x901A;&#x8FC7;&#x957F;&#x5EA6;&#x4E3A;<span class="mathjax-exps">$i$</span>&#x7684;&#x8DEF;&#x5F84;&#x8BBF;&#x95EE;&#x7684;&#x603B;&#x6B21;&#x6570;</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="1131" class="slide " data-line="1131" data-h="9" data-v="3">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">LNH&#x6307;&#x6570;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5BF9;&#x5145;&#x5206;&#x5927;&#x7684;<span class="mathjax-exps">$i$</span>&#x6709;<span class="mathjax-exps">$\lambda_1 \pv_i = \pv_{i+1}$</span>&#xFF1A;&#x8DEF;&#x5F84;&#x957F;&#x5EA6;&#x52A0;<span class="mathjax-exps">$1$</span>&#xFF0C;&#x8DEF;&#x5F84;&#x6570;&#x4E58;&#x4EE5;<span class="mathjax-exps">$\lambda_1$</span></p>
<div>
    $$
        \begin{align*}
            \Ebb [[\Av]^i_{uv}] = \frac{d_u d_v \lambda_1^{i-1}}{2 |\Ecal|}
        \end{align*}
    $$
</div>
<br>
<p>LNH &#x6307;&#x6570;</p>
<div>
    $$
        \begin{align*}
            [\Sv_{\text{LNH}}]_{uv} &amp; = [\Iv]_{uv} + \sum_{i=1}^\infty \frac{\Av^i}{\Ebb [\Av^i]} = [\Iv]_{uv} + \frac{2 |\Ecal| \lambda_1}{d_u d_v} \sum_{i=1}^\infty \beta^i \lambda_1^{-i} [\Av^i]_{uv} \\
            &amp; = \left( 1 - \frac{2 |\Ecal| \lambda_1}{d_u d_v} \right) [\Iv]_{uv} + \frac{2 |\Ecal| \lambda_1}{d_u d_v} \sum_{i=0}^\infty \beta^i \lambda_1^{-i} [\Av^i]_{uv}
        \end{align*}
    $$
</div>
<p>&#x7B2C;&#x4E00;&#x9879;&#x662F;&#x5BF9;&#x89D2;&#x9635;&#xFF0C;&#x4E0D;&#x4F53;&#x73B0;&#x4E24;&#x4E2A;&#x70B9;&#x4E4B;&#x95F4;&#x7684;&#x5173;&#x7CFB;&#xFF0C;&#x53EF;&#x4EE5;&#x7701;&#x7565;</p>
<div>
    $$
        \begin{align*}
            \Sv_{\text{LNH}} = 2 |\Ecal| \lambda_1 \Dv^{-1} ( \Iv - \beta \Av / \lambda_1 )^{-1} \Dv^{-1}, \quad \Dv = \diag \{ d_1, \ldots, d_{|\Vcal|} \}
        \end{align*}
    $$
</div>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section></section><section><section data-notes lineno="1182" class="slide " data-line="1182" data-h="10" data-v="0">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x968F;&#x673A;&#x6E38;&#x8D70;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x5229;&#x7528;&#x968F;&#x673A;&#x6E38;&#x8D70;&#x751F;&#x6210;&#x7684; Markov &#x94FE;&#x7684;&#x5E73;&#x7A33;&#x72B6;&#x6001;&#x8BBE;&#x8BA1;&#x76F8;&#x4F3C;&#x5EA6;</p>
<br>
<p>&#x5B9A;&#x4E49;&#x72B6;&#x6001;&#x8F6C;&#x79FB;&#x77E9;&#x9635;</p>
<div>
    $$
        \begin{align*}
            \Pv = \Av \Dv^{-1} = \begin{bmatrix}
                0                               &amp; 1_{(2,1) \in \Ecal} / d_2               &amp; \cdots &amp; 1_{(|\Vcal|,1) \in \Ecal} / d_{|\Vcal|} \\
                1_{(1,2) \in \Ecal} / d_1       &amp; 0                                       &amp; \cdots &amp; 1_{(|\Vcal|,2) \in \Ecal} / d_{|\Vcal|} \\
                \vdots                          &amp; \vdots                                  &amp; \ddots &amp; \vdots                          \\
                1_{(1,|\Vcal|) \in \Ecal} / d_1 &amp; 1_{(2,|\Vcal|) \in \Ecal} / d_2 &amp; \cdots &amp; 0
            \end{bmatrix}
        \end{align*}
    $$
</div>
<p>&#x5373;&#x5BF9;&#x4E8E;&#x4EFB;&#x610F;&#x70B9;&#xFF0C;&#x4EE5;&#x5747;&#x7B49;&#x7684;&#x6982;&#x7387;&#x6E38;&#x8D70;&#x5230;&#x67D0;&#x4E00;&#x90BB;&#x5C45;</p>
<br>
<ul>
<li><span class="mathjax-exps">$\Pv$</span>&#x5217;&#x548C;&#x4E3A;<span class="mathjax-exps">$1$</span>&#xFF0C;&#x79F0;&#x4E3A;<span class="blue">&#x5217;&#x968F;&#x673A;&#x77E9;&#x9635;</span></li>
<li><span class="mathjax-exps">$\ev^\top \Pv = \ev^\top$</span>&#xFF0C;&#x5373;<span class="mathjax-exps">$1$</span>&#x662F;&#x5176;&#x7279;&#x5F81;&#x503C;&#xFF0C;&#x5BF9;&#x5E94;&#x7684;&#x5DE6;&#x7279;&#x5F81;&#x5411;&#x91CF;&#x662F;<span class="mathjax-exps">$\ev^\top$</span></li>
</ul>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="1226" class="slide " data-line="1226" data-h="10" data-v="1">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x968F;&#x673A;&#x6E38;&#x8D70;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p>&#x82E5;<span class="mathjax-exps">$\Pv$</span>&#x5B58;&#x5728;&#x7279;&#x5F81;&#x503C;<span class="mathjax-exps">$\lambda \geq 1$</span>&#x4E14;<span class="mathjax-exps">$\vv^\top \Pv = \lambda \vv^\top$</span>&#xFF0C;&#x8BBE;<span class="mathjax-exps">$[\vv]_j = \max_i [\vv]_i$</span>&#xFF0C;&#x5219;</p>
<div>
    $$
        \begin{align*}
            [\vv]_j \leq \lambda [\vv]_j = \sum_i [\vv]_i [\Pv]_{ij} \leq \sum_i [\vv]_j [\Pv]_{ij} = [\vv]_j \sum_i [\Pv]_{ij} = [\vv]_j
        \end{align*}
    $$
</div>
<p>&#x5373;&#x82E5;<span class="mathjax-exps">$\lambda \geq 1$</span>&#xFF0C;&#x5FC5;&#x7136;&#x6709;<span class="mathjax-exps">$\lambda = 1$</span>&#x4E14;<span class="mathjax-exps">$\vv$</span>&#x7684;&#x6240;&#x6709;&#x5143;&#x7D20;&#x76F8;&#x7B49;&#xFF0C;&#x6545;<span class="mathjax-exps">$1$</span>&#x662F;&#x552F;&#x4E00;&#x7684;&#x6700;&#x5927;&#x7279;&#x5F81;&#x503C;</p>
<br>
<p>&#x53D6;<span class="mathjax-exps">$\qv_0$</span>&#x4E3A;&#x4EFB;&#x610F;&#x521D;&#x59CB;&#x6982;&#x7387;&#x5206;&#x5E03;&#xFF0C;&#x5E8F;&#x5217;<span class="mathjax-exps">$\{ \qv_i \}_{i=1}^\infty$</span>&#x6784;&#x6210; Markov &#x94FE;&#xFF0C;&#x8BBE;<span class="mathjax-exps">$\qv$</span>&#x662F;&#x5176;&#x5E73;&#x7A33;&#x72B6;&#x6001;&#xFF0C;&#x7531;&#x7EC6;&#x81F4;&#x5E73;&#x7A33;&#x6761;&#x4EF6;<span class="mathjax-exps">$[\Pv]_{ji} [\qv]_i = [\Pv]_{ij} [\qv]_j$</span>&#x77E5;</p>
<div>
    $$
        \begin{align*}
            [\qv]_i = [\qv]_i \overbrace{\sum_j [\Pv]_{ji}}^{=1} = \overbrace{\sum_j [\Pv]_{ji} [\qv]_i = \sum_j [\Pv]_{ij} [\qv]_j}^{\text{detailed balance condition}}
        \end{align*}
    $$
</div>
<p>&#x5199;&#x6210;&#x77E9;&#x9635;&#x7684;&#x5F62;&#x5F0F;<span class="mathjax-exps">$\qv = \Pv \qv$</span>&#xFF0C;&#x5373;&#x5E73;&#x7A33;&#x72B6;&#x6001;&#x5C31;&#x662F;&#x6700;&#x5927;&#x7279;&#x5F81;&#x503C;<span class="mathjax-exps">$1$</span>&#x5BF9;&#x5E94;&#x7684;&#x7279;&#x5F81;&#x5411;&#x91CF;</p>
<div class="footer">
    <hr class="hr_bottom">
    <div class="multi_column">
        <h6 class="bottom_left">&#x56FE;&#x795E;&#x7ECF;&#x7F51;&#x7EDC;&#x5BFC;&#x8BBA;</h6>
        <h6 class="bottom_center">&#x56FE;&#x673A;&#x5668;&#x5B66;&#x4E60;</h6>
        <h6 class="bottom_right">tengzhang@hust.edu.cn</h6>
    </div>
</div>
</section><section vertical="true" data-notes lineno="1270" class="slide " data-line="1270" data-h="10" data-v="2">
<div class="multi_column">
    <div class="title_hr"> 
        <hr class="hr_top">
        <h5 class="title">&#x968F;&#x673A;&#x6E38;&#x8D70;</h5>
    </div>
    <img class="xiaohui" src="../common/img/xiaohui.png" height="120px">
</div>
<p><!--?xml version="1.0" encoding="UTF-8" standalone="no"?-->

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</p><div style="margin-left:20%;margin-top:-18%;margin-bottom:3%">
$$
    \begin{align*}
        &amp; \Av = \begin{bmatrix} 
            0 &amp; 1 &amp; 1 &amp; 1 \\
            1 &amp; 0 &amp; 1 &amp; 0 \\
            1 &amp; 1 &amp; 0 &amp; 1 \\
            1 &amp; 0 &amp; 1 &amp; 0 \\
        \end{bmatrix}, ~ \Dv = \begin{bmatrix} 
            3 \\
            &amp; 2 \\
            &amp; &amp; 3 \\
            &amp; &amp; &amp; 2 \\
        \end{bmatrix}
        \\
        &amp; \begin{bmatrix} 
            0.3 \\ 0.2 \\ 0.3 \\ 0.2 \\
        \end{bmatrix} = \begin{bmatrix} 
            0 &amp; 1/2 &amp; 1/3 &amp; 1/2 \\
            1/3 &amp; 0 &amp; 1/3 &amp; 0 \\
            1/3 &amp; 1/2 &amp; 0 &amp; 1/2 \\
            1/3 &amp; 0 &amp; 1/3 &amp; 0 \\
        \end{bmatrix} \begin{bmatrix} 
            0.3 \\ 0.2 \\ 0.3 \\ 0.2 \\
        \end{bmatrix}
    \end{align*}
$$
</div>
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